How to Find the Area of a Pentagon With the Apothem

The Pentagon is a regular polygon.

Pentagons follow the same general rules of other polygons. The apothem is a length inside the polygon that measures distance from the center point to the middle of any side. A polygon has an apothem if and only if the polygon is regular, which means each side has an identical measurement. You can easily find a regular pentagon's area with its apothem by the formula for area is 1/2 * apothem length * perimeter, where the perimeter is the length around the pentagon.

Things You'll Need

• Calculator

Instructions

1. Multiply the length of a side by 5 to obtain the pentagon's perimeter. In this example, let the side measure 8, and 5 times 8 equals 40.

2. Multiply the perimeter by the length of the apothem. For this example, the apothem is approximately 5.5. Multiplication of 40 by 5.5 results in 220.

3. Divide the product of the apothem and perimeter in half. Concluding this example, dividing 220 by 2 results in 110. The area of the pentagon is 110.

References

• Dummies.com: Sizing Up the Area of a Polygon
• Math Open Reference: Apothem of a Regular Polygon
• Wolfram MathWorld: Regular Polygon