Last updated on July 25th, 2025
The perimeter of a shape is the total length of its boundary. The sum of all four sides is called the perimeter of a trapezium. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a trapezium.
The perimeter of a trapezium is the total length of its four sides. By adding the length of all four sides, we get the perimeter of the shape. The formula for the perimeter of a trapezium is ๐ = ๐ + ๐ + ๐ + ๐, where a, b, c, and d are the sides of the trapezium. For instance, if a trapezium has sides, a = 5, b = 7, c = 9, and d = 6, then its perimeter is P = 5 + 7 + 9 + 6 = 27.
Letโs consider another example of a trapezium with side lengths, ๐ = 8, ๐ = 12, ๐ = 10, and ๐ = 14. So the perimeter of the trapezium will be: ๐ท = ๐ + ๐ + ๐ + ๐ = 8 + 12 + 10 + 14 = 44.
To find the perimeter of a trapezium, we just need to apply the given formula and sum all the sides of the trapezium. For instance, a given trapezium has the sides of a = 7, b = 8, c = 5, d = 9. Perimeter = sum of all sides = 7 + 8 + 5 + 9 = 29 cm. Example Problem on Perimeter of Trapezium - For finding the perimeter of a trapezium, we use the formula, ๐ท = ๐ + ๐ + ๐ + ๐. For example, letโs say, a = 6 cm, b = 4 cm, c = 3 cm, and d = 5 cm. Now, the perimeter = sum of all sides = 6 + 4 + 3 + 5 = 18 cm Therefore, the perimeter of the trapezium is 18 cm.
Learning some tips and tricks makes it easier for children to calculate the perimeter of trapeziums. Here are some tips and tricks given below: Always remember that a trapezium's perimeter is simply the sum of the four sides of the shape. For that, use the formula, ๐ท = ๐ + ๐ + ๐ + ๐. Calculating the perimeter of a trapezium starts by determining the length of each side. If coordinates are given, use the distance formula: Distance = โ((x2-x1)ยฒ + (y2-y1)ยฒ). Here, (x1, y1) and (x2, y2) indicate the positions of two points that form a trapeziumโs side. They can be found by adding the lengths of four sides after they are calculated. To reduce confusion, arrange the indicated side lengths if you need the perimeter of a group of trapeziums. After that, apply the formula to each trapezium. To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture. If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations, like Heronโs formula, often use the semi-perimeter.
Did you know that while working with the perimeter of a trapezium, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
A trapezium-shaped park has a perimeter of 60 meters and three sides measuring 15 meters, 12 meters, and 18 meters. To find out the missing side, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 15 meters.
Let โdโ be the length of the missing side. And the given perimeter = 60 meters. Length of the three known sides = 15, 12, and 18 meters. Perimeter of trapezium = sum of lengths of four sides. 60 = 15 + 12 + 18 + d 60 = 45 + d d = 60 โ 45 = 15 Therefore, the missing side is 15 meters.
A piece of land with a perimeter of 150 meters is reshaped into a trapezium with one side measuring 40 meters and two parallel sides measuring 35 meters each. Find the length of the remaining side.
40 meters
Given that the perimeter of the land is equal to the sum of all sides of the trapezium, here is the solution: Perimeter of trapezium = Total length of the land Length of the land used = Perimeter of the trapezium formed Perimeter of trapezium = 40 + 35 + 35 + d 150 = 110 + d 150 - 110 = d d = 40 Therefore, the length of the remaining side of the trapezium is 40 meters.
Find the perimeter of a trapezium with sides measuring 10 cm, 12 cm, 8 cm, and 15 cm.
45 cm
Perimeter of trapezium = a + b + c + d P = 10 + 12 + 8 + 15 = 45 Therefore, the perimeter of the trapezium is 45 cm.
John wants to build a fence around his trapezium-shaped garden. The sides of the garden measure: Side A = 20 meters Side B = 25 meters Side C = 30 meters Side D = 15 meters How much fencing should John buy to go around the garden?
John will need 90 meters of fencing to go around the garden.
The perimeter of a trapezium is the sum of all four sides. Using the formula: P = a + b + c + d P = 20 + 25 + 30 + 15 = 90 meters.
Find the perimeter of a trapezium-shaped sheet of metal with sides measuring 14 cm, 11 cm, 9 cm, and 10 cm.
Perimeter = a + b + c + d = 14 + 11 + 9 + 10 = 44 cm.
Each side of the trapezium has a different length. The entire distance around the sheet is calculated to be 44 cm by summing the lengths of the four sides.
Perimeter: The total length of the sides of a shape. Trapezium: A quadrilateral with at least one pair of parallel sides. Isosceles Trapezium: A trapezium with equal non-parallel sides. Scalene Trapezium: A trapezium with all sides of different lengths. Formula of perimeter: The mathematical expression used to calculate the perimeter of a trapezium is ๐ท = ๐ + ๐ + ๐ + ๐.
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
: She has songs for each table which helps her to remember the tables