Question

Find the area of the

Answer 1

Answer:

Option E

Step-by-step explanation:

Central angles of a regular polygon = $\frac{360}{n}$

Here, n = Number of sides of the regular polygon

Therefore, central angle of the regular polygon = $\frac{360}{8}$ = 45°

From the picture attached,

m∠AOB = $\frac{45}{2}$ = 22.5°

By tangent rule,

tan(∠AOB) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(22.5°) = $\frac{AB}{OB}$

AB = OB[tan(22.5°)]

AB = 5(0.414213)

     = 2.07 in

Therefore, area of ΔAOC = 2 × (Area of ΔABO)

                                          = $2(\frac{1}{2})(\text{Base})(\text{Height})$

                                          = 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.