## Area of a Trapezoid Lesson

### 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.

INTRODUCING

### Area of a Trapezoid Example Problems

Let's go through a couple of example problems together to practice finding the area of a trapezoid.

#### Example 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:

- 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 **The area is 50.**

#### Example 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:

- 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 **The trapezoid's area is 20.**