Question

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

Answer 1

Use the regular octagon area formula (or split into 8 isosceles triangles). For circumradius R = 2:

Area = (1/2)·8·R^2·sin(360°/8) = 4·R^2·sin 45°
= 4·4·(√2/2) = 16·0.70710678 ≈ 11.31 ft^2.

Rounded, the best choice is 11.2 ft^2.