## Area of a trapezoid

How to find the area of a trapezoid.

 What is a trapezoid? A trapezoid is a four-sided figure that has one pair of parallel lines. In contrast with a triangle, which has only one base, a trapezoid has TWO bases. We call one of the bases "base 1" and the other "base 2".

The technique for finding the formula for the area of a trapezoid is the exact same technique we used for the triangles.

To find the area of this trapezoid, we double it to create a familiar parallelogram.

For this parallelogram, its base is the sum of the top and bottom bases of the trapezoid. So the area of the parallelogram is found like this

Area of parallelogram = $\large~(b_1 + b_2) • h$ = (2 + 6) • 3 = 24 square units

However, we only want the area of the trapezoid, so we have to divide the area of the parallelogram by 2 as such

Area of trapezoid = (Area of parallelogram) ÷ 2 = 24 ÷ 2 = 12 square units

To put this entire process on one line it would look like this

Area of trapezoid = (area of parallelogram) ÷ 2 = $\large~(b_1 + b_1)•h ÷ 2$

More often the formula looks like this

A = $\large~\frac{(b_1+b_2)•h}{2}$

 Find the area of this trapezoid. A = $\large~\frac{(b_1+b_2)•h}{2}=\frac{(6+3)•4}{2}=\frac{9•4}{2}=\frac{36}{2}=18\,u^2$

 Find the area of this trapezoid. A = $\large~\frac{(b_1+b_2)•h}{2}=\frac{(8+4)•2}{2}=\frac{12•2}{2}=\frac{24}{2}=12\,u^2$

 Directions: Move the blue vertices to create a trapezoid. Use the "Hint 1" slider to see how a trapezoid compares with a parallelogram. Use the "Hint 2" slider to see how to calculate the area of the trapezoid.

# Self-Check

 Question 1 Find the area of this trapezoid. [show answer] A = $\frac{(b_1+b_2)•h}{2}=\frac{(8+4)•3}{2}=\frac{12•3}{2}=\frac{36}{2}=18\,u^2$

 Question 2 Find the area of this trapezoid. [show answer] A = $\frac{(b_1+b_2)•h}{2}=\frac{(7+1)•3}{2}=\frac{8•3}{2}=\frac{24}{2}=12\,u^2$

 Question 3 Find the area of this trapezoid. [show answer] A = $\frac{(b_1+b_2)•h}{2}=\frac{(7+4)•5}{2}=\frac{11•5}{2}=\frac{55}{2}=27.5\,u^2$