The diagram shows a regular pentagon with side length s. Explore the area of this pentagon by following these steps.

✓ 1. Press Continue to partition the pentagon into five congruent triangles.

✓ 2. Press Continue to draw an apothem with length a.

✓ 3. Based on the variables on the diagram, how can the area of the shaded triangle be determined?
Area = sa 1/2sa 5s

✓ 4. Because the triangles are congruent, the area of the entire pentagon is equal to 0.5 2 5 times the area of the shaded triangle.

✓ 5. The area of the pentagon is #&{\sf 5}(\frac{\sf 1}{\sf 2}sa),#& or #&{\sf 5}s(\frac{\sf 1}{\sf 2}a).#&
The area perimeter side length of the pentagon is also equal to 5s.

✓ 6. Therefore, if the perimeter of the pentagon is p, the area of the pentagon can be found by this formula:

Area = #&\frac{\sf 1}{\sf 2}ap#&