Question

(Area formula I used is the image I provided)

Determine the area of each of the following polygons using the area formula you created in part d.



Polygon Area

regular pentagon with apothem of approximately 9 inches and side length of 13 inches

regular octagon with apothem of approximately 5 centimeters and side length of 4 centimeters

regular hexagon with apothem of approximately 6 feet and side length of 7 feet

Answer 1

1. The area of regular pentagon = 292.5 inches²

2. The area of the regular octagon = 80 cm²

3. The area of the regular hexagon = 126 feet²

Explanation:

∵ The area of any regular polygon = 1/2 × perimeter × apothem

1. Regular pentagon

∵ Regular pentagon has 5 equal sides

∵ The perimeter of the regular pentagon = 5 × side length

∵ S = 13 inches

∴ P = 13 × 5 = 65 inches

∵ apothem = 9 inches

∴ A = 1/2 × 65 × 9 = 292.5 inches²

2. Regular octagon

∵ Regular octagon has 8 equal sides

∵ The perimeter of the regular octagon = 8 × side length

∵ S = 4 cm

∴ P = 4 × 8 = 32 cm

∵ apothem = 5 cm

∴ A = 1/2 × 32 × 5 = 80 cm²

3. Regular hexagon

∵ Regular hexagon has 6 equal sides

∵ The perimeter of the regular hexagon = 6 × side length

∵ S = 7 feet

∴ P = 7 × 6 = 42 feet

∵ apothem = 6 feet

∴ A = 1/2 × 42 × 6 = 126 feet²