Question

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.

ft2

Answer 1

I don’t have the diagram you’re looking at, so I can’t be sure how B, C, I, H, F, and E are placed. Could you either

- upload the picture, or
- describe where each point lies (for example: “A and D are the endpoints of the diameter, O is the center, B and C are points on the semicircle so that arc BC = 45°, I and H are the foots of perpendiculars from B and C to the diameter,” etc.)?

If you can’t upload the picture, a short description of which points are on the semicircle, which are on the diameter, and what FE = 3 refers to will let me compute the requested area.

If the region BCIH is just the circular segment cut off by chord BC (i.e., the area between arc BC and chord BC) then with radius r = 6 and central angle 45° the area would be
- sector area = (45/360)·π·6^2 = (1/8)·36π = 4.5π ≈ 14.137
- isosceles triangle area = 1/2·r^2·sin45° = 1/2·36·(√2/2) = 9√2 ≈ 12.728
- segment area = sector − triangle ≈ 14.137 − 12.728 ≈ 1.409 ft^2 ≈ 1 ft^2 (to the nearest sq ft).

But that is just one possible interpretation; please upload or describe the diagram so I can give the correct area.