Question

The figure shows a circle inscribed into a regular pentagon.Cis the center of the circle and the regular pentagon.G and H are on the edge of both the circle and the regular pentagon.The radius of the circle is 3 inches.GHCPart A. Find the area of the dark shaded region. Show your work.Part B. Find the area of the light shaded region. Show your work.

Answer 1

Part A: The area of the dark shaded region = S1,

where

The radius of the circle is 3 inches.

`\begin{gathered} S_1=(4)/(5)\pi r^2 \\ =(4)/(5)\pi.3^2 \\ S_1=(36)/(5)\pi in^2 \end{gathered}`

Part B: The area of the light shaded region = S,

`\begin{gathered} S=S_2-S_1 \\ S=5*(1)/(2)r.rtan36 \\ S=(45)/(2)\sqrt{5-2√(5)} \\ S=(45)/(2)\sqrt{5-2√(5)}-(36)/(5)\pi in^2 \end{gathered}`