## 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.

$Are{a}_{trapezoid}=\frac{{b}_{1}+{b}_{2}}{2}\times h$, where ${b}_{1}\mathrm{and}{b}_{2}$ 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: $Are{a}_{trapezoid}=\frac{{b}_{1}+{b}_{2}}{2}\times h$$=\frac{7+11}{2}\times 5$$=\frac{18}{2}\times 5$$=9\times 5$$=45c{m}^{2}$

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

Solution: $Are{a}_{trapezoid}=\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.
- $Are{a}_{trapezoid}=\frac{{b}_{1}+{b}_{2}}{2}\times h$, 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.

- Fiona Wong
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