A stop sign is a regular octagon. The standard stop sign has a 16.2 inch radius. The area of a standard stop sign is
square inches. Please round your answer to the nearest whole number

The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

Step-by-step explanation:

The given is,

               Radius of standard stop sign is 16.2 inch radius

Step:1

              The regular octagon is equal to the 16 right angled triangle,

                    Angle of right angle triangle  = = 22.5°

              Ref attachment,

              From the OAB right angle triangle,  

              Trigonometric ratio,

                                 sin ∅ =        

              Where, ∅ = 22.5°

                           Hyp = Radius = 16.2 inches

              Ratio becomes,

                           sin 22.5°=

                                       b = (0.374607)(16.2)

                                       b = 6.19947 inches

             Trigonometric ratio,

                                 cos ∅ =        

              Where, ∅ = 22.5°

                           Hyp = Radius = 16.2 inches

                            Adj = h

              Ratio becomes,

                           cos 22.5°=

                                       h = (0.9238795)(16.2)

                                       h = 14.967 inches

Step:2

           From the triangle OAC,

                             Area,

          Where, Height = 14.967 inches

                       Base = b + x = 6.19947 + 6.19947

                                             = 12.3989 inches

           From the values equation becomes,

                                       A =

                                       A = 92.7875 Squared inches

Step:3

           The octagon is equal to sum of 8 triangles

            Area of octagon = 8 × Area of triangle

                                        = 8 × 92.7875

                                        = 742.3 squared inches

Result:

        The area of standard stop sign regular octagon is 742.3 squared inches, if the standard stop sign has a 16.2 inch radius.

Step-by-step explanation:

using Pythagoras theorem adjacent will be 15

so cos will be adjacent/hypotenuse

which is 15/17=0.882