The area of the shaded region in the given quadrant, to the nearest hundredth is: 4.57 ft².
What is the Area of a Quadrant?
Area of a quadrant = 1/4 × area of a circle = 1/4 × πr²
The figure has been partitioned into A, B, C to E.
The area of the shaded region = A + B
Step 1: Find the area of A:
Area of A = area of the square formed by D, A, and C - area of D + area of C.
Area of D = area of square - area of quadrant formed by A and C
Area of D = s² - 1/4 × πr² = 2² - 1/4 × π(2)²
Area of D = 0.86 ft²
Area D = area of C = 0.86 ft²
Area of D + area of C = 2(0.86) = 1.72 ft²
Area of A = 4 - 1.72 = 2.28 ft²
Step 2: Find the area of quadrants E and F
Area of quadrants E and F = 2(1/4 × πr²) = 2(1/4 × (3.14)(2)²)
Area of quadrants E and F = 6.28 ft².
Step 3: Find the area of B
Area of B = area of the biggest quadrant - area of quadrants E and F + area of square formed by D, A, and C
Area of B = 1/4 × πr² - 6.28 + 4
Area of B = 1/4 × π(4²) - 10.28
Area of B = 2.29 ft².
Step 4: Find the area of the shaded region
Area of the shaded region = A + B = 2.28 + 2.29
Area of the shaded region = 4.57 ft².
In conclusion, the area of the shaded region in the given quadrant, to the nearest hundredth is: 4.57 ft².
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