### Home > CCG > Chapter 12 > Lesson 12.2.3 > Problem12-86

12-86.

Find the area of the shaded region of the regular pentagon at right. Show all work.

Label the shaded region as $ΔABC$.

The measure of each angle in a pentagon is equal to $\frac{180(5 \cdot 2)}{5} = 180^\circ$.

Therefore, the measure of $\angle BAC$ is equal to $\frac{108}{3} = 36^\circ$

Divide $\Delta ABC$ into two triangles. Use a trigonometric ratio to solve for $AD$.

$\tan 18^\circ = \frac{2}{AD}$

$6.2$ units$^2$