Question

When BA = 10 ft, find the area of the region that is NOT shaded. Round to the nearest whole number.

A) 52 ft^2

B) 262 ft^2

C) 43 ft^2

D) 305 ft^2

Answer 1

(1) Area of the whole circle:
                        A = πr²
Substitute the value of BA to r,
                         A = (π)(10 ft)² = 314.16 ft²

(2) Area of the sector is calculated through the equation,
                       As = πr²(x/360°)
where x is the intercepted angle. Substituting the values,
                       As = π(10 ft)²(60°/360°) = 52.36 ft²

(3) Area of the equilateral triangle BAJ,
                      At = (√3)(a2²/4
where a is also equal to r or BA. Substituting,
                      At = (√3)(10 ft)²/4 = 43.30 ft²

The area of the region not shaded is equal to,
                 = (A) - (As - At)

Substituting,
                 = (314.16 ft²) - (52.36 ft² - 43.30 ft²)
                  Area = 305.10 ft²

Therefore, the answer to this answer is letter D.