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| Math Central | Quandaries & Queries |
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Question from Connie, a parent: How do you find surface area if the rectangle is 100ft. by 200ft. with quarter circles in the corners with a radius of 20ft? |
Hi Connie,
Start with a rectangle 100 feet by 200 feet which has area 100 × 200 square feet. From each corner remove a square which is 20 feet by 20 feet.
The area remaining is
100 × 200 - 4 × 20 × 20 = 20000 - 4 × 202 = 20000 - 1600 = 18400 square feet.
Take a circle of radius 20 feet, cut it into four quarter circles and place the quarter circles in the missing corners of the rectangle.
The area of a circle of radius 20 feet is π × 202 square feet so the area of the rectangle with rounded corners is
18400 + π × 202 = 18400 + 1256.6 = 19656.6 square feet.
Penny
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