### Home > GC > Chapter 12 > Lesson 12.2.3 > Problem12-77

12-77.

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

Label the shaded region as ∠ABC.

$\textrm{The measure of each angle in a pentagon}$

$\textrm{is equal to} \frac{180(5\cdot 2)}{5}=180^{\circ}.$

$\textrm{Therefore the measure of } \angle A$

$\textrm{is equal to } \frac{108}{3}=36^{\circ}.$

Divide ΔABC into two triangles. Use a trigonometric ratio to solve for AD.

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

Find the area of ΔABC now that you know the lengths of both its base and height.

6.2 units²