Answer:
Option E
Step-by-step explanation:
Central angles of a regular polygon = [tex]\frac{360}{n}[/tex]
Here, n = Number of sides of the regular polygon
Therefore, central angle of the regular polygon = [tex]\frac{360}{8}[/tex] = 45°
From the picture attached,
m∠AOB = [tex]\frac{45}{2}[/tex] = 22.5°
By tangent rule,
tan(∠AOB) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(22.5°) = [tex]\frac{AB}{OB}[/tex]
AB = OB[tan(22.5°)]
AB = 5(0.414213)
= 2.07 in
Therefore, area of ΔAOC = 2 × (Area of ΔABO)
= [tex]2(\frac{1}{2})(\text{Base})(\text{Height})[/tex]
= AB × OB
= 2.07 × 5
= 10.35 in²
Since, area of the given regular octagon = 8 × (Area of ΔAOC)
= 8(10.35)
= 82.5 in²
Therefore, Option (E) is the answer.
