108 LearnersLast updated on August 5th, 2025
Perimeter of Isosceles Trapezium
The perimeter of a shape is the total length of its boundary. The sum of all four sides is called the perimeter of an isosceles trapezium. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of an isosceles trapezium.
What is the Perimeter of an Isosceles Trapezium?
The perimeter of an isosceles 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 an isosceles trapezium is ๐ = ๐ + ๐ + 2๐, where a and b are the parallel sides, and c is the length of the non-parallel sides (equal). For instance, if an isosceles trapezium has parallel sides a = 6, b = 8, and non-parallel sides c = 5, then its perimeter is P = 6 + 8 + 2(5) = 24.
Formula for Perimeter of Isosceles Trapezium - ๐ = ๐ + ๐ + 2๐.
Letโs consider another example of an isosceles trapezium with parallel side lengths ๐ = 10, ๐ = 14, and non-parallel sides ๐ = 7. So the perimeter of the trapezium will be: ๐ = ๐ + ๐ + 2๐ = 10 + 14 + 2(7) = 38.
How to Calculate the Perimeter of an Isosceles Trapezium
To find the perimeter of an isosceles 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 = 8, b = 12, and c = 6. Perimeter = sum of all sides = 8 + 12 + 2(6) = 32 cm. Example Problem on Perimeter of Isosceles Trapezium - For finding the perimeter of an isosceles trapezium, we use the formula, ๐ = ๐ + ๐ + 2๐. For example, letโs say, a = 9 cm, b = 5 cm, and c = 3 cm. Now, the perimeter = sum of all sides = 9 + 5 + 2(3) = 20 cm. Therefore, the perimeter of the isosceles trapezium is 20 cm.
Tips and Tricks for Perimeter of Isosceles Trapezium
Learning some tips and tricks makes it easier for children to calculate the perimeter of isosceles trapeziums. Here are some tips and tricks given below: Always remember that an isosceles trapeziumโs perimeter is simply the sum of the four sides of the shape. For that, use the formula, ๐ = ๐ + ๐ + 2๐. Calculating the perimeter of an isosceles trapezium starts by determining the length of each side, ensuring the pair of non-parallel sides are equal. To reduce confusion, specifically 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 often use the semi-perimeter, although not directly for trapeziums.
Common Mistakes and How to Avoid Them in Perimeter of Isosceles Trapezium
Did you know that while working with the perimeter of an isosceles trapezium, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly assuming all sides are equal in length.
Remember that only the non-parallel sides of an isosceles trapezium are equal. The lengths of the parallel sides can differ and should be calculated or measured accordingly.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the trapeziumโs sides, while the area, in square units, represents the space inside the trapezium.
Mistake 3
Assuming that every trapezium is isosceles, which results in inaccurate calculations.
A scalene trapezium has all sides of different lengths. Always be careful about the type of the trapezium to ensure accurate calculations.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your trapezium.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw a trapezium to accurately identify the side lengths.
Perimeter of Isosceles Trapezium Examples
Problem 1
A garden bed is shaped like an isosceles trapezium with a perimeter of 50 meters. The lengths of the parallel sides are 15 meters and 20 meters. To find out the length of the non-parallel sides, subtract the sum of the known sides from the total perimeter and divide by 2.
Length of each non-parallel side = 7.5 meters.
Explanation
Let โcโ be the length of each non-parallel side. And the given perimeter = 50 meters. Length of the parallel sides = 15 meters and 20 meters. Perimeter of trapezium = sum of lengths of four sides. 50 = 15 + 20 + 2c 50 = 35 + 2c 2c = 50 โ 35 = 15 c = 7.5 Therefore, each non-parallel side is 7.5 meters.
Problem 2
A wire with a perimeter of 80 inches is reshaped into an isosceles trapezium. If the length of one parallel side is 30 inches and the other is 20 inches, find the length of the non-parallel sides.
15 inches
Explanation
Given that the perimeter of the wire is equal to the total length of the trapezium formed: Perimeter of the trapezium = Total length of the wire Length of the wire used = Perimeter of the trapezium formed Perimeter of an isosceles trapezium = ๐ + ๐ + 2c 80 = 30 + 20 + 2c 80 = 50 + 2c 2c = 30 c = 15 Therefore, the length of each non-parallel side is 15 inches.
Problem 3
Find the perimeter of an isosceles trapezium whose parallel sides are 12 cm and 8 cm, and non-parallel sides are 5 cm.
30 cm
Explanation
Perimeter of trapezium = a + b + 2c P = 12 + 8 + 2(5) = 30 Therefore, the perimeter of the trapezium is 30 cm.
Problem 4
Sam is designing a walkway in his backyard in the shape of an isosceles trapezium. The walkway's parallel sides are 18 meters and 12 meters, and the non-parallel sides are each 9 meters. How much edging material should Sam purchase to go around the walkway?
Sam will need 48 meters of edging material to go around the walkway.
Explanation
The perimeter of an isosceles trapezium is the sum of all the four sides. Using the formula: P = a + b + 2c P = 18 + 12 + 2(9) = 48 meters.
Problem 5
Find the perimeter of an isosceles trapezium with parallel sides 20 cm and 10 cm and non-parallel sides 6 cm.
52 cm
Explanation
Each non-parallel side of the isosceles trapezium is equal in length. The entire distance is calculated around the trapezium by summing the lengths of the four sides. Perimeter = a + b + 2c = 20 + 10 + 2(6) = 52 cm.
FAQs on Perimeter of Isosceles Trapezium
1.Evaluate the trapeziumโs perimeter if its parallel sides are 15 cm, 10 cm, and non-parallel sides are 4 cm.
2.What is meant by an isosceles trapeziumโs perimeter?
3.What are the types of trapeziums?
4.Which trapezium has no equal non-parallel sides?
5.Which trapezium has a pair of equal non-parallel sides?
Important Glossaries for Perimeter of Isosceles Trapezium
Perimeter: The total length of the sides of a shape. Isosceles Trapezium: A quadrilateral with one pair of parallel sides and the other pair of sides equal in length. Parallel Sides: The two sides of the trapezium that are parallel to each other. Non-parallel Sides: The two sides of the trapezium that are not parallel but are equal in length in an isosceles trapezium. Formula of Perimeter: The mathematical expression used to calculate the perimeter of an isosceles trapezium is ๐ = ๐ + ๐ + 2๐.
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Seyed Ali Fathima S
About the Author
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.
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: She has songs for each table which helps her to remember the tables
