How to Calculate the Area of Regular Polygons

The area of a regular polygon is half the apothem times the perimeter. The apothem is the distance from the center to the middle of a side, and that formula works because the polygon splits into identical triangles.

• Regular Triangle (Equilateral): Area (A = frac{sqrt{3}}{4} times text{side}^2)

• Regular Quadrilateral (Square): Area (A = text{side}^2)

• Regular Pentagon: Area (A = frac{5}{4} times frac{text{side}^2}{tan(frac{180}{5})})

• Regular Hexagon: Area (A = frac{3sqrt{3}}{2} times text{side}^2)

Examples

Practice Questions:

1. Find the area of an equilateral triangle with a side length of (9 text{ cm}).
2. What is the area of a square with a side of (10 text{ cm})?
3. Determine the area of a regular hexagon with each side measuring (5 text{ cm}).
4. For a regular triangle (equilateral) with a side length of (9 text{ cm}) and an apothem of (7.79 text{ cm}), calculate its area.
5. What is the area of a square with a side of (10 text{ cm}) and an apothem of (7.07 text{ cm})?
6. Determine the area of a regular pentagon with each side measuring (11 text{ cm}) and an apothem of (9 text{ cm}).

1. ( 35.07 text{ cm}^2 )
2. ( 100 text{ cm}^2 )
3. ( 64.95 text{ cm}^2 )
4. ( 105.21 text{ cm}^2 )
5. ( 141.4 text{ cm}^2 )
6. ( 247.5 text{ cm}^2 )

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