7th Grade - Area of Trapezoids

Introduction

A trapezoid or trapezium is a quadrilateral that has only one pair of opposite sides parallel.
These parallel sides are called bases and the remaining non-parallel sides are called legs.

There are two types of trapezoids:

1. Right Trapezoids: If one leg of a trapezoid makes a pair of right angles with the two bases, it is called a right trapezoid.

2. Isosceles Trapezoids: If the legs of a trapezoid are equal, it is called an isosceles trapezoid.

Area of Trapezoids

The area of a trapezoid is the region enclosed by its four sides.
The area of a trapezoid depends upon the measure of its bases and height.
If we know the length of the bases, and the height of a trapezium, we can determine its area using the formula mentioned below.

$A r e a_{t r a p e z o i d} = \frac{b_{1} + b_{2}}{2} \times h$ , where $b_{1} and b_{2}$ are the length of bases, and $h =$ height.

The perimeter of a trapezoid is the sum of the length of all its sides.

Some Solved Examples

Question 1: Find the area of the trapezium shown in the figure below.

Solution: $A r e a_{t r a p e z o i d} = \frac{b_{1} + b_{2}}{2} \times h$ $= \frac{7 + 11}{2} \times 5$ $= \frac{18}{2} \times 5$ $= 9 \times 5$ $= 45 c m^{2}$

Question 2: Find the area of the trapezium shown in the figure below.

Solution: $A r e a_{t r a p e z o i d} = \frac{b_{1} + b_{2}}{2} \times h$ $= \frac{5 + 10}{2} \times 6$ $= \frac{15}{2} \times 6$ $= 15 \times 3$ $= 45 m^{2}$

Cheat Sheet

The legs of an isosceles trapezoid are equal.
The perimeter of a trapezoid is the sum of all its sides.
$A r e a_{t r a p e z o i d} = \frac{b_{1} + b_{2}}{2} \times h$ , where $b_{1}, b_{2} =$ length of bases, and $h =$ height of the trapezoid

Blunder Areas

To find the area of a trapezoid, correctly identify its bases and height first.
Note that the height of a trapezoid is perpendicular to both bases.