501 Geometry Questions
- Area≈14.88 square feet.The shaded area is the difference of
ΔBCD’s area and the area between chord BD and arc BD. The
height of ΔBCD is 6 feet. Its area is ^12 (6 ×8) = 24 sq. ft. The area
of BD is tricky. It is the area of the circle contained within ∠BFD
minus the area of inscribed ΔBFD. Central angle BFD is a right
angle; it is a quarter of a circle’s rotation and a quarter of its area.
The circle’s radius is 4 2 feet. The area of circle F is
π(4 2 ft.)^2 , or 32πsquare feet. A quarter of that area is 8πsquare
feet. The area of ΔBFD is ^12 (4 2 × 4 2 ) = 16 sq. ft. Subtract 16
square feet from 8πsquare feet, then subtract that answer from 24
square feet and your answer is approximately 14.88 square feet.
501 Geometry Questions
