CPM Homework Help : INT2 Problem 9-89

The United State Department of Defense is located in a building called the Pentagon because it is in the shape of a regular pentagon. Known as “the largest office building in the world,” its exterior edges measure $921$ feet.

What is the area of land enclosed by the outer walls of the Pentagon building?

If 1 mile is equal to $5280$ feet, what is that area in square miles?

Step 1:

Draw a sketch of the situation:

A regular pentagon with a side 921 feet.

The pentagon is divided into 5 equal triangles from the center point.

Added to the divided pentagon, From the center point, a perpendicular segment to one of the sides.

Step 2:

Divide the pentagon into 5 equal isosceles triangles:

Step 3:

Draw a height for one of the triangles, dividing it into two right triangles:

Step 4:

Find the area using trigonometric ratios.

The legs of a right triangle are 460.5 ft and h. The angle opposite leg, h, is theta.

Hint:

The interior angles of a regular pentagon measure $\frac{180(5-2)}{5}=\frac{180\cdot3}{5}=\frac{540}{5}=108^\circ$

More help:

$\Theta = \frac{108^\circ}{2}$