Geometry

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# Area of a Trapezoid

## Trapezoid Area Formula

The formula for area of a trapezoid is given as:**A = ^{1}⁄_{2}h(a + b)**

Where

*A*is the area,

*h*is the height,

*a*is the short base, and

*b*is the long base.

### Example Problems

**Problem 1:**

The two bases of a trapezoid are 4 and 6 long. The height is 10. What is the area of the trapezoid?

Solution:

1.) Plugging the given values into the area formula, we get:

A = ^{1}⁄_{2}h(a + b)

A = ^{1}⁄_{2}(10)(4 + 6) = (5)(10) = 50

2.) **The area is 50.**

**Problem 2:**

A trapezoid is made up of a square with an area of 10 and two congruent triangles with an area of 5 each. What is the area of the trapezoid?

Solution:

1.) We have the area of all three shapes that compose the trapezoid. Therefore, we can add them together to find the trapezoid’s area.

A = a1 + a2 + a3

A = 10 + 5 + 5 = 20

3.) **The trapezoid’s area is 20.**

Result :

Worksheet 1

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Cheat sheet

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