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Trapezoid Formula with Solved Examples

A trapezoid is also called a trapezium which has a four-sided polygon or a quadrilateral. Explore more about trapezoids with solved examples.

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Trapezoid Formula with Solved Examples

A Trapezoid is a quadrilateral that includes one set of parallel sides and one set of non-parallel sides. The parallel sides of the trapezoid are called bases and the non-parallel sides are called as legs of the trapezoid. There are three types of trapezoids. They are as follows: –

Isosceles Trapezoid: – A trapezoid that consists of two non-parallel sides of similar length is known as an isosceles trapezoid.
Right Trapezoid: – A right Trapezoid is a type of trapezoid that consists of at least two right angles.
Scalene Trapezoid: – Scalene Trapezoid is the type of trapezoid in which the angles or sides are not similar nor equal to each other.

What is Trapezoid Formula

There are two types of formulas used in Trapezoid sums. They are as follows: –

Perimeter of Trapezoid
Area of Trapezoid

Formula to find Perimeter of Trapezoid

The perimeter of the Trapezoid is described as the sum of all sides of the trapezoid or the sum of the complete boundary of the trapezoid. Take a trapezoid PQRS with sides named P, Q, R, and S. The perimeter of the Trapezoid could be encountered by summing up all the sides of the trapezoid.

PQ+RS+QR+SR

The perimeter of the Trapezoid= P+Q+R+S

Here, P, Q, R, and S are the sides of the trapezoid.

The formula of Area of Trapezoid

The area of the trapezoid is described as the area or region covered by the trapezoid. It is half of the product of sum of its bases and the distance between them. If there is a trapezoid named ABCD

Then, Area of Trapezoid= 1/2 × h (a+b)

Here a = shorter base

b = longer base

h = height or distance between them

Therefore, Area of Trapezoid= a+b/2 ×h

Solved Examples

Example 1

If the perimeter of a trapezoid is given as 80 units where its sides are 20 units, 15 units, and 18 units. Now find out the fourth side with help of the Trapezoid formula.

Given: – Perimeter= 80 units

a = 20 units, b = 15 units, c = 18 units

The perimeter of the Trapezoid = 80

a + b + c + d = 80

20 + 15 + 18 + d = 80

d = 27 units

Example 2

Bases of a trapezoid are given as 19 and 15 units respectively; the height is given as 8 units. Now find out the area of a trapezoid with the help of the Trapezoid formula.

Bases a = 19 units

b = 15 units

h = 8 units

Area of trapezoid = 19+15/2 × 8

Area of trapezoid= 136-unit sq