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Home > CCG > Chapter 12 > Lesson 12.2.1 > Problem 12-62


The United States 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 feet. Find the area of land enclosed by the outer walls of the Pentagon building.  

A regular pentagon with a side 921 feet.

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

From the center point a perpendicular line is dropped to one of the sides.

Find the area using trigonometric ratios.

The perpendicular line is, h, forming a right angle with the base of the right triangle, 460.5 feet. Angle theta is opposite the side, h.

The interior angles of a regular pentagon measure