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 = 4
5°. Find the area of the glass in region BCIH, rounded to the nearest square foot.
2 answers:
Answer:
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
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