Find the area of the regular figure below:

A) 67.3 in2
B) 70.2 in2
C) 74.6 in2
D) 77.1 in 2
E) 82.8 in2

pls show work

Option E

Step-by-step explanation:

Central angles of a regular polygon =

Here, n = Number of sides of the regular polygon

Therefore, central angle of the regular polygon = = 45°

From the picture attached,

m∠AOB = = 22.5°

By tangent rule,

tan(∠AOB) =

tan(22.5°) =

AB = OB[tan(22.5°)]

AB = 5(0.414213)

     = 2.07 in

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

                                          =

                                          = 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.

a

step-by-step explanation:

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