Question

Pls asap... use trigonometry to find the area of a regular 20- gon with each side = 6 in

Answer 1

Answer:

Area of polygon[20 sides] = 1,140 inch² (Approx.)

Step-by-step explanation:

Given;

Number of sides = 20 sides

Length of each side = 6 inch

Find:

Area of polygon[20 sides]

Computation:

Perimeter of polygon[20sides] = 20 x Length of each side

Perimeter of polygon[20sides] = 20 x 6

Perimeter of polygon[20sides] = 120 inch

Apothem[Shortest distance from center] = S / 2tan[180/n]

Apothem[Shortest distance from center] = 6 / 2tan[180/20]

Apothem[Shortest distance from center] = 6 / 2tan[9]

Apothem[Shortest distance from center] = 18.94

Apothem[Shortest distance from center] = 19 inch (Approx.)

Area of polygon[20 sides] = [Perimeter x Apothem] / 2

Area of polygon[20 sides] = [120 x 19] / 2

Area of polygon[20 sides] = 1,140 inch² (Approx.)