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kondor19780726 [428]
3 years ago
9

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.

Mathematics
2 answers:
Alex3 years ago
5 0

Answer:

11 feet to the nearest square foot.

Step-by-step explanation:

The area of sector BCG

= 45/180 * 1/2 π r^2

= 1/4 * 1/2 π r^2

= 1/8 * π * 6^2

= 4.5 π ft^2.

The radius of the inner semicircle is 6 - 3 = 3 feet.

The area of sector HIG = 1/4 * 1/2 π  3^2

= 1.125 π ft^2.

So the area of BCIH

= area of BCG - area HIG

=  4.5  π - 1.125  π

=  3.375  π

= 10.6 square feet.

Sergeu [11.5K]3 years ago
3 0

Answer:

The area of the glass in region BCIH is 11 to the nearest feet²

Step-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

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