Answer:
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 = [tex]8\times \frac{1}{2}\cdot apothem \cdot base[/tex]
We have to apothem as,
Measure of central angle of an octagon is [tex]\frac{360}{8}=45^{\circ}[/tex]
Thus, Apothem is ,
Using trigonometric ratio,
[tex]\cos22.5^{\circ}=\frac{a}{2}[/tex]
Simplify for a,
We have,
[tex]\cos22.5^{\circ} \cdot 2=a[/tex]
Thus, Area of window is
Area of window = [tex]8\times \frac{1}{2}\cdot \cos22.5^{\circ} \cdot 2 \cdot 1.52[/tex]
Thus, Area of window is 11.2 ft²
