Manuel wants to buy a window shade to cover the window and frame shown. the window is in the shape of a regular the radius of the window, including the frame, is 2 ft, and the measure of each edge of the octagonal frame is 1.52 frame octagon.
what is the approximate area of the window that needs to be covered, including the frame?
a. 2 ft2
b. 7 ft2
c. 11.2 ft2
d. 22.5 ft2

Option (c) is correct.

Area of window is 11.2 ft²

Step-by-step explanation:

Given : A window in shape of a regular octagon and a frame having measure of each edge length 1.52 ft.

We have to  find the  approximate area of the window that needs to be covered.

Consider the given octagonal window.

Since, The edge length of window is 1.52

Perimeter = 1.52 × 8 = 12.16 ft

Area of window = 8 × Area of each triangle.

Area of window =

We have to apothem as,

Measure of central angle of an octagon is

Thus, Apothem is ,

Using trigonometric ratio,

Simplify for a,

We have,

Thus, Area of window is

Area of window =

Thus, Area of window is 11.2 ft²

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step-by-step explanation:

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.