How to find perimeter - We will discuss here how to find the perimeter of a square. Perimeter of a square is the total length (distance) of the boundary of a square.

 
We can calculate the perimeter of a sector by adding together the lengths of the two radii and the arc length of the sector. E.g.. Calculate the perimeter of .... Cable tricep extension

The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is …To use the parallelogram perimeter calculator, follow the steps: Determine which part of the calculator is the one you need. Assume it's the second part. Type the values – in this case, side (a) and two diagonals (e, f): 15 in, 18 in, and 24 in, respectively. If you enter the values which can't form the parallelogram, the calculator will tell ...Review related articles/videos or use a hint. Report a problem. Do 4 problems. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. The perimeter of an object is the measurement of the sides of the object. Measuring the perimeter of a square or rectangle is easy, but measuring the perimeter of a cube is slightl...To find the angle of any regular polygon, you find the number of sides, . In this example . You then subtract from the number of sides, yielding . Take and multiply it by to yield the total number of degrees in the regular hexagon. Then, to find one individual angle, we divide by the total number of angles, . The answer is .Perimeter is the boundary covered around a 2-dimensional object. The cylinder being a 3-dimensional shape, we cannot practically find the perimeter of a cylinder. However, in the case of a cylinder, we can find the perimeter by making a vertical cross-section along the line, parallel to its height, such that it forms a rectangle.The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths. The perimeter of the quadrilateral ... An easy to use, free perimeter calculator you can use to calculate the perimeter of shapes like square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, octagon, and sector of a circle. Formulas, explanations, and graphs for each calculation. Perimeter of a triangle calculation using all different rules: SSS, ASA, SAS, SSA, etc. Learn how to find the perimeter of a shape when one or more of the sides are missing. Use clues, such as the length of a side or the shape of a figure, to estimate the missing …Perimeter of a Triangle = Sum of all three sides. The perimeter formulas for different types of triangles are: Perimeter of a Scalene Triangle = a + b + c, where a, b, and c are the three different sides. Perimeter of an Isosceles Triangle = 2a + b, where a is the length of each of the two sides of equal length and b is the third side.The perimeter of a trapezoid. A trapezoid is a quadrilateral with at least two parallel sides called bases. While the other two are called legs. To find the perimeter of a trapezoid, we need to know the values of bases and legs. The formula for the perimeter of a trapezoid is: P=a+b+c+d. Trapezoid.If one wants to find the perimeter of, for example, a triangle with vertices A ( x A , y A ) , B ( x B , y B ) , and C ( x C , y C ) , the distance formula can ...The perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. When you are given the dimensions of a rectangular shape, you can simply plug in the values of L and W into the formula in order to solve for the perimeter.For the figure below, the perimeter is: P = s 1 + s 2 + s 3 + s 4. s 1 s 2 s 3 s 4. The area, A , of a polygon is the amount of flat space inside the polygon's edges. Area is measured in square units such as square miles. Different polygons have their own area formulas. The volume, V , of an object is the amount of space that object occupies.Find its perimeter. Solution: To Find: Perimeter of the kite. Given: a = 12 inch b = 15 inch Now, using the perimeter of a kite formula: Perimeter = 2(a+b) Perimeter = 2(12+15) Perimeter = 2(27) Perimeter = 54 inches. Answer: Perimeter of the kite is 54 inches. Example 2: The sides of a kite are in the ratio of 3:5. If the side smaller among ...We can calculate the perimeter of a sector by adding together the lengths of the two radii and the arc length of the sector. E.g.. Calculate the perimeter of ...Once one of the sides has been found, the perimeter can be solved for by multiplying the side length by the number of sides (. In order to solve for the side (or as some call it, the base side), we can use right triangles. The first step is to solve for the internal angles of the hexagon. This can be solved through is the number of sides.Perimeter. = a + b + a + b. = 2a + 2b. The perimeter of a rectangle: To find the perimeter of a rectangle, just add up all the lengths of the sides: Perimeter = L + w + L + w. = 2L + 2w. The perimeter of a rhombus: To find the perimeter of …Possible Answers: To find the perimeter of any rectangle, add all of the sides up: 20 + 20 + 12 + 12 = 64 inches. You could use this formula as well: , where P = perimeter, l = …Explanation: . We know that .. We also know that since is a square, all of its sides are of equal length. To get the measure of any one side of , take the square root of the area: centimeters. Therefore each side of is 14 centimeters long. …Nov 21, 2023 ... Thanks for checking out that quick explanation of perimeter.3rd grade 14 units · 141 skills. Unit 1 Intro to multiplication. Unit 2 1-digit multiplication. Unit 3 Addition, subtraction, and estimation. Unit 4 Intro to division. Unit 5 Understand fractions. Unit 6 Equivalent fractions and comparing fractions. Unit 7 More with multiplication and division. Unit 8 Arithmetic patterns and problem solving. Learn the definition, formulas, and examples of perimeter, the total length of a shape's boundary. Find out how to calculate the perimeter of regular and irregular polygons, and see real-world applications of perimeter in geometry and real life. Make your home feel like part of the natural landscape. Whether you’re into classic, well-manicured American suburban landscape design, or favor a more natural look featuring nativ...The perimeter of a trapezoid. A trapezoid is a quadrilateral with at least two parallel sides called bases. While the other two are called legs. To find the perimeter of a trapezoid, we need to know the values of bases and legs. The formula for the perimeter of a trapezoid is: P=a+b+c+d. Trapezoid.Learn how to calculate the perimeter of a two-dimensional shape, such as a triangle, a square, a circle or an ellipse. Find the formulas for different shapes and practice with interactive exercises. Example: Find the perimeter of a sector whose area is 324 square units and the radius is 27 units. Solution: Let us find the perimeter of the sector using the following steps: We know that, Area of a Sector of Circle = 1/2 × r 2 θ, where, θ is the sector angle subtended by the arc at the center, in radians, and 'r' is the radius of the circle.May 19, 2023 · Multiply the side length by 4 to find the perimeter. Take the side length s you just calculated and plug it into the perimeter formula, P = 4s. The result will be the perimeter of your square! For the square with area 20 and side length 4.472, the perimeter P = 4 * 4.472, or 17.888. Learn the definition, formulas, and examples of perimeter, the total length of a shape's boundary. Find out how to calculate the perimeter of regular and irregular polygons, and see real-world applications of perimeter in geometry and real life. Video transcript. We are told that the formula for finding the perimeter of a rectangle is P is equal to 2l plus 2w, where P is the perimeter, l is the length, and w is the width. And just to visualize what they're saying, and you might already be familiar with this, let me draw a rectangle. That looks like a rectangle.Feb 8, 2021 ... Answer ... Answer: -To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height ...Example: If the perimeter of a trapezoid is 24 units and the rest of its sides are given as follows: 5 units, 7 units, 4 units, let us find the missing side. Step 1: Write the given dimensions of the trapezoid. Perimeter = 24 units, Side 1 = 5 units, Side 2 = 7 units, Side 3 = 4 units. Step 2: Assume the missing side length of the trapezoid to ...The easiest way to calculate the number of acres in your land is to use the calculator above. If you know the length and width, simply enter them. The calculator will provide the number of acres, as well as the area in other units. To calculate acres by hand, multiply your length and width (in feet) to get square feet. 3rd grade 14 units · 141 skills. Unit 1 Intro to multiplication. Unit 2 1-digit multiplication. Unit 3 Addition, subtraction, and estimation. Unit 4 Intro to division. Unit 5 Understand fractions. Unit 6 Equivalent fractions and comparing fractions. Unit 7 More with multiplication and division. Unit 8 Arithmetic patterns and problem solving.Intro Finding the Perimeter | Math with Mr. J Math with Mr. J 1.03M subscribers Subscribe Subscribed 3.8K 459K views 4 years ago Measurement Learn …To find the perimeter of a polygon, take the sum of the length of each side. The polygons below are much smaller than a fenced-in yard. Thus, we use smaller ...The perimeter of a trapezoid. A trapezoid is a quadrilateral with at least two parallel sides called bases. While the other two are called legs. To find the perimeter of a trapezoid, we need to know the values of bases and legs. The formula for the perimeter of a trapezoid is: P=a+b+c+d. Trapezoid.Examples: find the perimeter of a triangle. Example 1: In the simplest scenario one has measured all three sides of a triangle and then it is a matter of simple summation to find the perimeter. For example, if the sides are 3 in, 4 in, and 5 in, then the perimeter is simply 3 + 4 + 5 = 12 inches in total.Finding the Perimeter of a Shape. Step 1: Look at the given figure, and identify the lengths of all of the sides of the figure. Step 2: Add all the side lengths together to find the perimeter of ... The formula is created by halving the circle perimeter formula (circumference) and adding the diameter length to that. Perimeter of a full circle is P = 2πr, so half of that is πr, which gives us the top arc's length for the semicircle. The bottom side of the semicircle is equal to the circle's diameter, so it is 2r since d = 2r.The formula to find the perimeter of a square is given by: The perimeter of Square = 4s units. Substitute the value of ‘s’ in the perimeter formula, P= 4 × 5 cm. P = 20 cm. Therefore, the perimeter of square = 20 cm. Question 2: Calculate the perimeter of a square having a side of 16 cm. Solution: Given, Side of the square = a = 16 cm If one wants to find the perimeter of, for example, a triangle with vertices A ( x A , y A ) , B ( x B , y B ) , and C ( x C , y C ) , the distance formula can ...Calculate the perimeter of a parallelogram using our Perimeter Calculator, or try calculating it yourself with the formulas provided. Geometry Calculator. Enter the base and side of the parallelogram in the calculator below to …Download Article. 1. Use the formula C = πd to find the circumference if you know the diameter. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its ...Perimeter is the boundary covered around a 2-dimensional object. The cylinder being a 3-dimensional shape, we cannot practically find the perimeter of a cylinder. However, in the case of a cylinder, we can find the perimeter by making a vertical cross-section along the line, parallel to its height, such that it forms a rectangle.Find the perimeter and area of circle whose radius is 5 cm. [Note: π = 3.14] Solution: To find: Perimeter and area of circle. Given that, Radius, r = 5 cm and π = 3.14. As we know, the circumference (or) perimeter of a circle = …Use this perimeter calculator to easily calculate the perimeter of common bodies like a square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, regular octagon, and sector of a circle. Learn the formulas and …The perimeter is the distance all the way around the outside of a 2D shape. To work out the perimeter, add up the lengths of all the sides. The perimeter of this shape is 10 + 10 + 6 + 6 = 32 ... 1. Remember the formula for finding the perimeter of a triangle. For a triangle with sides a, b and c, the perimeter P is defined as: P = a + b + c. [2] What this formula means in simpler terms is that to find the perimeter of a triangle, you just add together the lengths of each of its 3 sides. 2.To find the perimeter of a trapezoid if you know the length of both sides and the bases, add together the length of all 4 sides. If you know the height, both side lengths, and the top base length, draw a straight line down from each top corner to form a square and 2 triangles. Then, use the Pythagorean Theorem to find the length of the base of ...The process is simple. 1. Type the height into the “Height” field. 2. Type the width into the “Width” field. 3. Select the unit used for the height and width measurements in the convenient Input Units drop-down box. 4. Select the unit you wish to use in the Output Units drop-down box.To find the perimeter of a quadrilateral on a graph, we use the following steps. Step 1: Find the coordinates of the vertices from the graph. Step 2: Apply the distance formula to find the side lengths of the quadrilateral. Step 3: Add all the side lengths and the sum gives the perimeter of the quadrilateral.A different formula is required to work out the perimeter of a semi circle (a circle cut in half), because it consists of a curved edge as well as a straight edge. That formula is. P = \frac {1} {2} πd + d P = 21πd +d. where d is the diameter of the semi circle. Apply the number pi (π) to the formula. P = 1 2 π d + d.Perimeter of an Ellipse. On the Ellipse page we looked at the definition and some of the simple properties of the ellipse, but here we look at how to more accurately calculate its perimeter.. Perimeter. Rather strangely, the perimeter of an ellipse is very difficult to calculate!. There are many formulas, here are some interesting ones.Find the perimeter of the rectangle below. We will work the perimeter out using the 3 different ways above: Add up the lengths of each side separately: 7 + 2 + 7 + 2 = 18. Double the lengths of the adjacent sides and add them: double 7 + double 2 = 14 + 4 = 18. Add the adjacent sides and double the answer: double (7 + 2) = double 9 = 18.Jan 15, 2023 · Perimeter is always expressed in the same linear measurement used for the lengths of sides. Perimeter of a rectangle formulas How to find the perimeter of a rectangle. Here we have a rectangle with four vertices, D, U, C, K. Rectangle DUCK. Sides DU and KC are congruent and parallel. Sides DK and UC are also congruent and parallel. That is why ... Jan 18, 2024 ... How can you calculate the perimeter of a rectangle whose area is 20 m^2 and length is 4 m? · Find the width w by diving the area A=20 cm^2^ by ...Well, how to find perimeter of different shapes is no more complex with our free perimeter to area calculator. What is Perimeter? In mathematics, the perimeter of a shape is defined as the total distance around the shape. Basically, it is the length of any shape, as long as it is expanded linearly. The range of various shapes can be the same in ...Finding the Perimeter of a Shape. Step 1: Look at the given figure, and identify the lengths of all of the sides of the figure. Step 2: Add all the side lengths together to find the perimeter of ... Apr 6, 2017 ... For lesson plans and activities that go along with this video, visit https://rb.gy/feozdh. This outer space-themed video teaches the ...Use this perimeter calculator to easily calculate the perimeter of common bodies like a square, rectangle, triangle, circle, parallelogram, trapezoid, ellipse, regular octagon, and sector of a circle. Learn the formulas and …Learn how to calculate the perimeter of any closed shape using a formula and practice with worksheets. Perimeter is the total length of the boundary of a shape, while area …The perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. When you are given the dimensions of a rectangular shape, you can simply plug in the values of L and W into the formula in order to solve for the perimeter.Perimeter of a Triangle = Sum of all three sides. The perimeter formulas for different types of triangles are: Perimeter of a Scalene Triangle = a + b + c, where a, b, and c are the three different sides. Perimeter of an Isosceles Triangle = 2a + b, where a is the length of each of the two sides of equal length and b is the third side.Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.Nov 9, 2020 ... How to find perimeter when I know acreage? · 10 x 10 => Perimeter = 40 · 5 x 20 => Perimeter = 50 · 1 x 100 => Perimeter = 202 ·...Example 1: calculate the perimeter of a sector (quadrant) Calculate the perimeter of a sector of the sector. Give your answer to 3 3 decimal places. Find the length of the diameter/radius. Radius = 6cm = 6cm. 2 Find the size of the angle creating the arc of the sector. Angle = 90^o = 90o.Learn how to find the perimeter of different shapes by adding up the lengths of the sides or multiplying the side length by the number of sides. See examples, tips, questions and …To find the perimeter of an equilateral triangle given its area, we must first find the length of the sides. This can be done by using the equation of the area of an equilateral triangle: where a is the side of the triangle. Because the sides of the equilateral triangle are equal, the perimeter is equal to 3a. Learn the definition and formula of perimeter, and how to add up the lengths of all the sides of a shape. Watch a video, do activities and quizzes to test your skills.To find the perimeter, add up the lengths of all the sides of the polygon. Finding the area can be a little more complicated, since it depends on what kind of …Perimeter of Trapezium = Sum of all Sides of Trapezium. Perimeter of Trapezium = 15 cm + 17 cm + 2 (8) = 15 cm + 17 cm + 16 cm. Perimeter of Trapezium = 48 cm. Example 5: Calculate the perimeter of a trapezium having parallel sides 25 cm and 30 cm. The non-parallel sides are 19 cm and 18 cm.Example 2: A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the perimeter. Solution 1: P = 8 cm + 8cm + 3 cm + 3 cm = 22 cm. Solution 2: P = 2 (8 cm) + 2 (3 cm) = 16 cm + 6 cm = 22 cm. In Example 2, the second solution is more commonly used. In fact, in mathematics, we commonly use the following formula for perimeter ... For the figure below, the perimeter is: P = s 1 + s 2 + s 3 + s 4. s 1 s 2 s 3 s 4. The area, A , of a polygon is the amount of flat space inside the polygon's edges. Area is measured in square units such as square miles. Different polygons have their own area formulas. The volume, V , of an object is the amount of space that object occupies. the perimeter. In order to calculate perimeter, you need to add together the lengths of all four. sides of the rectangle. You are given the length of one side and the width of one. side. Remember, opposite sides of a rectangle are equal, so really you already have. the measures of each side. Learn how to find the perimeter of a shape when one or more of the sides are missing. Use clues, such as the length of a side or the shape of a figure, to estimate the missing …To find the perimeter (the total distance around the square), add all the side lengths: 3 + 3 + 3 + 3 = 12 . Since each side of a square is the same, you can also multiply one side length by 4 to calculate the perimeter: 3 \times 4=12. 2 …Jan 16, 2024 · To find the perimeter of a trapezoid if you know the length of both sides and the bases, add together the length of all 4 sides. If you know the height, both side lengths, and the top base length, draw a straight line down from each top corner to form a square and 2 triangles. The perimeter of a polygon can be found by using the following steps: Step 1: Find whether the given polygon is a regular polygon or not. Step 2: If it is a regular polygon, the perimeter can be calculated using the formula, Perimeter of regular polygon = (number of sides) × (length of one side). For the figure below, the perimeter is: P = s 1 + s 2 + s 3 + s 4. s 1 s 2 s 3 s 4. The area, A , of a polygon is the amount of flat space inside the polygon's edges. Area is measured in square units such as square miles. Different polygons have their own area formulas. The volume, V , of an object is the amount of space that object occupies.Jan 18, 2024 · Learn how to find the perimeter of a square, a rectangle, a triangle, a circle, and more with this online calculator. Enter some numbers and get the perimeter formulas, definitions, and examples for each shape. The perimeter of a trapezoid. A trapezoid is a quadrilateral with at least two parallel sides called bases. While the other two are called legs. To find the perimeter of a trapezoid, we need to know the values of bases and legs. The formula for the perimeter of a trapezoid is: P=a+b+c+d. Trapezoid.Show step. Counting the units, the length of the rectangle is 6 6 units and the width of the rectangle is 8 8 units. To find the perimeter, add up all the side lengths. 6+6+8+8=28 6 + 6 + 8 + 8 = 28. OR. You can use the formula to find the …Intro Finding the Perimeter | Math with Mr. J Math with Mr. J 1.03M subscribers Subscribe Subscribed 3.8K 459K views 4 years ago Measurement Learn …P = D + πr. Where D = the diameter of the semi-circle and two times the radius. r = radius, which is often half the diameter. π = a constant equal to 3.142. The formula for the perimeter of the circle is derived from that of the full circle. The perimeter of a complete circle is the same as the circumference of the circle and is given as. P ...May 19, 2023 · Multiply the side length by 4 to find the perimeter. Take the side length s you just calculated and plug it into the perimeter formula, P = 4s. The result will be the perimeter of your square! For the square with area 20 and side length 4.472, the perimeter P = 4 * 4.472, or 17.888. Learn how to find the area and perimeter of rectangles using unit squares, formulas, and decomposing shapes. Practice with quizzes, exercises, and word problems to master …For the figure below, the perimeter is: P = s 1 + s 2 + s 3 + s 4. s 1 s 2 s 3 s 4. The area, A , of a polygon is the amount of flat space inside the polygon's edges. Area is measured in square units such as square miles. Different polygons have their own area formulas. The volume, V , of an object is the amount of space that object occupies. Sep 27, 2023 ... A rhombus has 4 sides, all equal in length. So, measure the length of one side and multiply that by 4 and you will have the perimeter. · For ...To find the perimeter of non-standard shapes, you still find the distance around the shape by adding together the length of each side. Finding the area of non-standard shapes is a bit different. You need to create regions within the shape for which you can find the area, and add these areas together. Have a look at how this is done below.

Jan 18, 2024 · To find the perimeter of a triangle knowing its three sides (SSS triangle), all you have to do is add the three known sides. For example, the perimeter of a triangle with sides a = 3 cm, b = 2 cm and c = 4 cm can be calculated as follows: perimeter_SSS = a + b+ c. perimeter_SSS = 3 cm + 2 cm + 4 cm. perimeter_SSS = 9 cm . Fabric cafe

how to find perimeter

Unit test. Level up on all the skills in this unit and collect up to 1800 Mastery points! Start Unit test. Area and perimeter help us measure the size of 2D shapes. We’ll start with the area and perimeter of rectangles. From there, we’ll tackle trickier shapes, such as triangles and circles. The perimeter of a triangle is the total distance around its three outer sides. If a triangle has side lengths equal to D, E and F, then its perimeter is the addition of D, E and F...Simply select the shape you are using, then enter the required information in the form fields. Our calculator will do the calculations for you. If you are trying to measure the perimeter and don’t have access to this calculator just remember that perimeter is the length of all the sides of a shape or the distance around the shape.We can calculate the perimeter of a sector by adding together the lengths of the two radii and the arc length of the sector. E.g.. Calculate the perimeter of ...May 19, 2018 ... This math video tutorial provides a basic introduction into area and perimeter. It explains how to calculate the area of a rectangle as well ...Example: If the perimeter of a trapezoid is 24 units and the rest of its sides are given as follows: 5 units, 7 units, 4 units, let us find the missing side. Step 1: Write the given dimensions of the trapezoid. Perimeter = 24 units, Side 1 = 5 units, Side 2 = 7 units, Side 3 = 4 units. Step 2: Assume the missing side length of the trapezoid to ... We calculate the perimeter of a rectangle by getting the sum of all its sides. How to Find the Perimeter of a Rectangle. As we all know, a rectangle has four sides and four right angles. However, when compared to a square, not all of its side measurements are equal. Two pairs of opposite sides in a rectangle have equal measurements.Feb 8, 2021 ... Answer ... Answer: -To find the perimeter of a rectangle, add the lengths of the rectangle's four sides. If you have only the width and the height ...annie, to find the perimeter of a semicircle on top of a triangle, you have to know 3 things: 1) The word "semicircle" literally means "half of a circle". 2) The formula for calculating the perimeter of a circle (Which is pi*d, where d is going to be the diameter of the circle --- or in our case the semicircle, and pi means the number π -- or ... For the figure below, the perimeter is: P = s 1 + s 2 + s 3 + s 4. s 1 s 2 s 3 s 4. The area, A , of a polygon is the amount of flat space inside the polygon's edges. Area is measured in square units such as square miles. Different polygons have their own area formulas. The volume, V , of an object is the amount of space that object occupies. Perimeter of a polygon is the total length of its boundary. Formula for the area of a polygon is different for different polygons. Examples: Area of a square = ( S i d e) 2 Area of a rectangle = length × width. We can give the generalized formula to find the perimeter of a polygon as: Perimeter of a polygon = Sum of all sides.To calculate the perimeter for any isosceles trapezoid: Perimeter of an isosceles trapezoid = length of opposite side x 2 + length of top base + length of bottom base. A stepped polygon. Stepped polygons have a very peculiar characteristic. The sum of the lengths of the sides that are parallel to the base measure the same as the length of the base.The Perimeter of a Rectangle ... To find the perimeter of a rectangle, add all the sides together or multiply 2(l + w). ... A rectangle has opposite sides that are ...Perimeter is the distance around the sides of a polygon or other shape. Perimeter is always the same linear measurement unit as the unit used for the sides. Perhaps one of the easiest ways to work with polygons is to find their perimeter, or the distance around their sides. The triangle is the simplest polygon, so finding its ….

Popular Topics