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How to find the perimeter of a trapezium?

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Trapezium is a quadrilateral in which one pair of opposite sides are parallel. The perimeter of trapezium is the sum of the boundaries of the trapezium. Suppose the sides of the trapezium are , b, c, and d then the perimeter of the trapezium is (a + b + c + d) units.

In this article, we will learn about What is Trapezium? Perimeter of Trapezium, Examples, and others in detail.

What is a Trapezium?

Trapezium is a quadrilateral containing one pair of opposite sides to are parallel in nature. These parallel sets of sides are called bases and the non-parallel sides of a trapezium are called legs. It can be considered as a special case of a parallelogram with two parallel sides. The other name of Trapezium is Trapezoid. 

Types of Trapezium

The trapezium can be categorized into three types that include,

  • Isosceles Trapezium
  • Scalene Trapezium
  • Right Trapezium

Properties of Trapezium

Various Properties associated to a Trapezium is,

  • One pair of opposite sides are parallel.
  • Unequal non-parallel sides. Exception is the isosceles trapezium.
  • The diagonals intersect each other.
  • The line that intersects the mid-points of the non-parallel sides is always parallel to the bases. These are equal to half of the sum of parallel sides

Perimeter of Trapezium

The total summation of the length of the boundary of the trapezoid or trapezium is referred to as the Perimeter of Trapezium. Trapezium is an irregular polygon so we have no fixed formula to calculate the perimeter of trapezium. The unit of the perimeter of the trapezoid is the unit of length, such as “inches”, “feet”, “metres” etc.

Perimeter of Trapezium = Sum of Non-Parallel Sides + Sum of Parallel Sides

How to Find Perimeter of Trapezium?

The perimeter of Trapezoid can be found by following the steps added below,

Step 1: Note all the dimensions of the given Trapezium.

Step 2: Find the sum of all the dimensions of the trapezium.

Step 3: Put the unit of perimeter as the same unit as the length of the trapezium.

Formula of Perimeter of Trapezoid

Let us assume a trapezoid ABCD, where we have sides AB and CD parallel to each other. They form the pair ‘bases’ while AD and BC are non-parallel sides (that is, they are legs). Let us assume the perimeter of the trapezoid is “P” units. The image of the assume trapezoid is added below,

Trapezium ABCD

Perimeter of trapezoid ABCD is given by,

 P = AB + BC + CD + AD

Perimeter of Trapezoid in terms of Area is given by the formula,

 P = (Sum of Lengths of Non-Parallel Sides) + 2 (A/h)

where,

  • A is Area of Trapezoid
  • h is Height

Read More,

Solved Examples on Perimeter of Trapezium

Example 1: Calculate the perimeter of a trapezium having parallel sides 4 cm and 6 cm. The non-parallel sides 5 cm and 8 cm?

Solution:

Given,

  • Parallel sides are 4 cm and 6 cm
  • Non-parallel sides are 5 cm and 8 cm

Perimeter of Trapezium is sum of all sides of Trapezium

Perimeter of Trapezium = Sum of Parallel Sides + Sum of Non-Parallel Sides

Perimeter of Trapezium = 4 cm + 6 cm + 5 cm + 8 cm

Perimeter of Trapezium = 23 cm

Example 2: Calculate the perimeter of a trapezium ground having parallel side 20 m 25 m and non-parallel side 18 m and 16 m?

Solution:

Given,

  • Parallel sides are 20 m and 25 m
  • Non-parallel sides are 18 m and 16 m

Perimeter of Trapezium is sum of all sides of Trapezium

Perimeter of Trapezium Ground = Sum of Parallel Sides + Sum of Non-Parallel Sides

Perimeter of Trapezium Ground = 20 m + 25 m + 18 m + 16 m

Perimeter of Trapezium Ground = 79 m

Example 3: If the perimeter of the trapezium is 54 cm and the parallel sides are 10 cm and 15 cm. Assume that the non-parallel sides are equal. Then find the length of both of the non-parallel sides?

Solution:

Given,

  • Perimeter of Trapezium 54 cm
  • Parallel sides are 10 cm and 15 cm

Non-parallel sides are equal, let assume non-parallel side be x

Therefore,

Perimeter of Trapezium = 54 cm

Perimeter of Trapezium = 10 cm + 15 cm + x + x

54 = 25 + 2x

2x = 54 – 25

2x = 29 

x = 29/2 = 14.5 cm

Therefore the non-parallel sides of the trapezium are 14.5 cm and 14.5 cm.

Example 4: Calculate the perimeter of the regular trapezium having the parallel side 15 cm 17 cm, the length of the non-parallel side is 8 cm.

Solution:

Given,

  • Parallel side of Trapezium are 15 cm and 17 cm
  • Length of Non-Parallel sides are 8 cm and 8 cm

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.

Solution:

Given,

  • Parallel sides are 25 cm and 30 cm
  • Non-parallel sides are 19 cm and 18 cm

Perimeter of Trapezium we need to add all the sides of the trapezium.

Perimeter of trapezium = Sum of Parallel Sides + Sum of Non-Parallel Sides

Perimeter of trapezium = 25 cm + 30 cm + 19 cm + 18 cm

Perimeter of trapezium = 92 cm

Practice Questions on Perimeter of Trapezium

Q1. Find the perimeter of the trapezium of sides, 12 units, 14 units, 20 units, and 16 units.

Q2. What is the perimeter of the trapezium of sides with sides 2 units, 4 units, 7 units, and 6 units?

Q3. What is the perimeter of Isosceles trapezium with equal sides 8 cm and other sides 9 cm and 7 cm?

Q4. If the perimeter of an Isosceles Trapezium is 60 cm and the unequal sides measures 22 and 14 cm then find the equal sides.

FAQs on Perimeter of Trapezium

1. What is a Trapezium?

Trapezium is a quadrilateral with one pair of parallel sides and the other pair is not parallel, they can be equal. The name of trapezium is derived from Greek word “trapeze” that means table.

2. What are Types of Trapezium?

There are generally two types of trapezium,

  • Regular Trapezium
  • Irregular Trapezium

3. What is Perimeter of Trapezium?

The perimeter of the trapezium is the sum of all the sides of the trapezium. It is also explain as the length of boundary of the trapezium.

Perimeter of Trapezium = Sum of All Sides

4. What is Formula for Perimerter of Trapezium?

Suppose we have a trapezium of sides a, b, c, and d units then the perimeter of the trapezium formula is,

Perimeter of Trapezium = (a + b + c + d) units

5. What is the Primeter of an Isosceles Trapezium?

In an isosceles trapezium, two sides are equal hence the perimeter of an Isosceles Trapezium is a + b + 2c where a and b are parallel sides and c is equal sides



Last Updated : 27 Sep, 2023
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