The window shown is the shape of a semicircle with a radius of 6 feet. The distance from F to E is 3 feet and the measure of = 45°. Find the area of the glass in region BCIH, rounded to the nearest square foot.

Answer:The area of the glass in region BCIH is 11 to the nearest feet²Step-by-step explanation:* Lets explain the figure- The window is a semicircle with center G and radius 6 feet- There is a small semicircle with center G and radius GF∵ GE is 6 feet and EF is 3 feet∵ GE = GF + FE∴ 6 = GF + 3 ⇒ subtract 3 from both sides∴ 3 = GF∴ The radius of the small semicircle is 3 feet∵ m∠BGC = 45°- The area of sector BGC is part of the area of the semicircle∵ The area of semi-circle is 1/2 π r²∵ The measure of the central angle of the semicircle is 180°∵ The measure of the central angle of the sector BGC is 45°∴ The sector = 45°/180° = 1/4 of the semi-circle∴ The area of the sector is 1/4 the area of the semicircle∵ The area of the semicircle = 1/2 π r²∵ r = 6 feet∴ The area of the semicircle = 1/2 π (6)² = 1/2 π (36) = 18 π feet²∴ Area of the sector = 1/4 (18 π) = 4.5 π feet²- The small sector HGI has the same central angle of the sector BGC∴ The area of the sector HGI is 1/4 The area of the small semicircle∵ The area of the small semicircle = 1/2 π r²∵ r = 3 feet∴ The area of the small semicircle = 1/2 π (3)² = 1/2 π (9) = 4.5 π feet²∴ Area of the sector HGI= 1/4 (4.5 π) = 1.125 π feet²- The area of the glass in region BCIH is the difference between the   area of sector BGC and the area of the sector HGI ∴ The area of the glass in region BCIH = 4.5 π - 1.125 π ≅ 11 feet²