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. What is the approximate area of the window that needs to be covered, including the frame? These are the answers

2 ft2
7 ft2
11.2 ft2
22.5 ft2

Answer 1

11.2 sq.ft.

Explanation:

We are given the window is in the shape of a regular octagon.

The radius of the window, including the frame, is 2 ft.

The measure of each edge of the octagonal frame is 1.52 ft.

Since the diagonals of regular octagon divides into 8 equal triangles

Two radii and one side forms one triangle.

We are supposed to find the approximate area of the window that needs to be covered, including the frame

Area of window including frame = Area of 8 triangles

So, first we need to find the area of 1 small triangle.

Heron's formula

Area of triangle =
`√(s(s-a)(s-b)(s-c))`

where a ,b and c are the sides of triangle

`s =(a+b+c)/(2)`

Substitute

`s=(2+2+1.52)/(2)`

`s=2.76`

So, Area of triangle =
`√(2.76\left(2.76-2\right)\left(2.76-2\right)\left(2.76-1.52\right))`

Area of triangle =
`1.4059`

Area of 8 equal triangles =
`1.4059 * 8 = 11.2 ft^2`

So, Area of window including frame=11.2 sq.ft.

Hence the approximate area of the window that needs to be covered, including the frame is 11.2 sq.ft.