Answer:
192.5 ft²
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.