MATH SOLVE

3 months ago

Q:
# (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 Arearegular pentagon with apothem of approximately 9 inches and side length of 13 inchesregular 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

Accepted Solution

A:

Answer:1. The area of regular pentagon = 292.5 inches²2. The area of the regular octagon = 80 cm²3. The area of the regular hexagon = 126 feet²Step-by-step explanation:∵ The area of any regular polygon = 1/2 × perimeter × apothem1. 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 inches²2. 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 cm²3. 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