Trapezoid Area Formula

The formula for area of a trapezoid is given as:

A = ¹⁄₂h(a + b)

Where A is the area, h is the height, a is the short base, and b is the long base.

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:

1. Plugging the given values into the area formula, we get:
   A = ¹⁄₂h(a + b)
   A = ¹⁄₂(10)(4 + 6) = (5)(10) = 50
2. 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:

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
2. The trapezoid's area is 20.