Question

A trapezoid has an area of 140 square centimetres and bases of 15 centimetres and 20 centimetres. What is the height of the trapezoid?

Short answer

The height of the trapezoid is 8 centimeters.

Step-by-step solution

Step 1. Given Information.

Area of a trapezoid: 140 centimetres

Base of a trapezoid: 20 centimetres

Step 2. Formula used.

$\text{Area of a trapezoid}=\frac{1}{2}\left(b_1+b_2\right)h$, where$b_1$, $b_2$ are the bases of the trapezoid andhis the height of the trapezoid.

Step 3. Calculation.

The height of the trapezoid can be calculated as:

$\begin{array}{c}\text{Areaofatrapezoid}=\frac{1}{2}\left(b_1+b_2\right)h\left[\text{Formulafortheareaofatrapezoid}\right]\\ 140=\frac{1}{2}\left(15+20\right)h\left[\text{substitutethegivenvalues}\right]\\ 140=\frac{35}{2}h\left[\text{add}\right]\\ 140\times 2=\frac{35}{2}h\times 2\left[\text{multiplybothsidesby2}\right]\\ \frac{280}{35}=\frac{35h}{35}\left[\text{dividebothsidesby35}\right]\\ h=8\left[\text{simplify}\right]\end{array}$

Step 4. Conclusion.

The height of the trapezoid is 8 centimeters.