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.

11 ft^2

Step-by-step explanation:

In the first figure attached, a graphical representation of the problem can be seen.

The area of the glass in region BCIH is equivalent to 1/8 of the "ring" area formed by the subtraction of the smaller circle to the bigger circle (see the second figure attached).

The number 1/8 comes from knowing that a circle form an angle of 360° and the angle between segments GC and GB is 45°, then, the area of the region of interest is 45°/360° = 1/8 respect the entire "ring".

The segment GF plus segment FE is equal to the radius of the bigger circle, which is 6 ft . Therefore,

GF + FE = 6 ft

GF = 6 ft - 3 ft

GF = 3 ft

"Ring" area is equal to the subtraction of the smaller circle area to the bigger circle area. Mathematically:

Ring area = pi*(6 ft)^2 - pi*(3 ft)^2

Ring area = 84.78 ft^2

Area of the glass in region BCIH = (1/8)*84.78 ft^2 = 11 ft^2