# How do you find the area of a trapezoid when you have the length of every side but not the height?

Nov 14, 2015

$\frac{B + b}{B - b} \cdot \Delta$

#### Explanation:

The triangle area is $\Delta = \frac{1}{2} \left(B - b\right) h = \sqrt{p \left(p - x\right) \left(p - y\right) \left(p - B + b\right)}$

$2 p = x + y + B - b$

This is Heron's formula. Solve for $h = \frac{2 \Delta}{B - b}$

Area of trapezoid = $\frac{B + b}{2} \cdot h$

$= \frac{B + b}{B - b} \cdot \sqrt{p \left(p - x\right) \left(p - y\right) \left(p - B + b\right)}$