Find the area of the regular figure below:

A) 466 mm2
B) 430 mm2
C) 404 mm2
D) 495 mm2
E) 512 mm2

explain pls

Option A

Step-by-step explanation:

Central angle of the pentagon =

                                                   =

                                                   = 72°

Measure of ∠BAC = 72°

Therefore, measure of ∠BAD =

                                                 = 36°

By sine rule in ΔABD,

sin(36°) =

            =

            =

BD = 14(sin36°)

     = 8.23 mm

Similarly, by cosine rule,

cos(36°) =

              =

              =

AD = 14(cos36°)

     = 11.33 mm

Area of ΔABC = 2(Area of ΔABD)

                        =

                        = AD × BD

                        = 11.33 × 8.23

                        = 93.21 mm²

Since, area of regular pentagon given in the picture = 5(area of ΔABC)

= 5(93.21)

= 466 mm²

Therefore, Option A will be the answer.

step-by-step explanation: yes

squares, rhombus, rectangles