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. A smaller hexagon is inside of a larger hexagon. The radius of the larger hexagon is 2 feet and the sides lengths of 1.52 feet. What is the approximate area of the window that needs to be covered, including the frame? 2 ft2 7 ft2 11.2 ft2 22.5 ft2

The approximate area of the window that needs to be covered, including the frame is 11.2ft² (Option C). This is derived using knowledge of the area of an octagon.

What is the area of a octagon?

The area of an octagon is given as:

2 × s2 × (1+√2).

Where "s" is indicative of the length of the sides of the octagon.

What then is the solution to the above?

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

A ≈ 11.2ft²

Learn more about the area of an octagon at:
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