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erma4kov [3.2K]
3 years ago
7

Please help me with this

Mathematics
1 answer:
liubo4ka [24]3 years ago
5 0

Answer:

  192.5 ft²

Step-by-step explanation:

The large sector of the circle has a central angle measure of 360° -100° = 260°, so its area will be (260°/360°) of the circle, or ...

  large sector area = (260/360)πr² = 13π/18·(8.35 ft)² ≈ 158.195 ft²

The area of the 100° triangle is ...

  triangle area = (1/2)r²·sin(100°) = (1/2)(8.35 ft)²·sin(100°) ≈ 34.332 ft²

Then the shaded area is ...

  shaded area = large sector area + triangle area

  = 158.195 ft² +34.332 ft² ≈ 192.5 ft²

The shaded area is about 192.5 square feet.

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