In the area formula for a regular polygon A = (1/2) × P × a, what does P represent?

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Multiple Choice

In the area formula for a regular polygon A = (1/2) × P × a, what does P represent?

P represents the perimeter—the total length around the polygon. You can see this by splitting the regular polygon into congruent triangles from the center. Each triangle has base equal to a side of the polygon and height equal to the apothem, so its area is (1/2) × (side length) × (apothem). Adding up all those triangle areas gives A = (1/2) × (sum of all side lengths) × apothem = (1/2) × P × apothem. Since the sum of all side lengths around the figure is the perimeter, P is the perimeter. The radius is the distance from the center to a vertex, and the apothem is the distance from the center to a side, not the total around the figure.

P represents the perimeter—the total length around the polygon. You can see this by splitting the regular polygon into congruent triangles from the center. Each triangle has base equal to a side of the polygon and height equal to the apothem, so its area is (1/2) × (side length) × (apothem). Adding up all those triangle areas gives A = (1/2) × (sum of all side lengths) × apothem = (1/2) × P × apothem. Since the sum of all side lengths around the figure is the perimeter, P is the perimeter. The radius is the distance from the center to a vertex, and the apothem is the distance from the center to a side, not the total around the figure.

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