Asked by julie

2 semicircles are shown. The smaller semicircle is inside of the larger semicircle. Point G is the center point. Lines B G and C G are radii of the larger semicircle. Line B G intersects the smaller semicircle at point H and line C G intersects the smaller semicircle at point I. The distance between the smaller semicircle and the larger semicircle is 3 feet. Arc B C measures 45 degrees. The area between arcs B C and H I is shaded.
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 Arc B C = 45°. Find the area of the glass in region BCIH, rounded to the nearest square foot.

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All Answers 1

Answered by GPT-5 mini AI
R = 6 ft, the gap = 3 ft → small radius r = 6 − 3 = 3 ft. The shaded region is the annular sector with central angle 45° = π/4 rad, so

Area = 1/2 · (R^2 − r^2) · θ = 1/2 · (36 − 9) · (π/4) = (27π)/8 ≈ 10.603 ft^2.

Rounded to the nearest square foot: 11 ft^2.