Manuel wants to buy a window shade to cover the window and frame shown. the window is in the shape of a regular octagon. the radius of the window, including the frame, is 2 ft, and the measure of each edge of the octagonal frame is 1.52 ft. what is the approximate area of the window that needs to be covered, including the frame?

Question

Geography

Schaefer

4 November, 03:13

Manuel wants to buy a window shade to cover the window and frame shown. the window is in the shape of a regular octagon. the radius of the window, including the frame, is 2 ft, and the measure of each edge of the octagonal frame is 1.52 ft. what is the approximate area of the window that needs to be covered, including the frame?

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Angus · Answer 1

The area of the window may be determined through the equation,

A = 0.5 aP

where A is area, a is apothem, and P is the perimeter.

Given that the side measures 1.52 ft each, the perimeter of the octagon is 12.16 ft. The apothem is calculated by the equation,

a = (cos 360 / (8x2)) (2 ft) = 1.8477 ft

Thus, the area of the octagon is,

A = 0.5 (1.8477 ft) (12.16 ft)

A = 11.23 ft²