# Find the area of a circle circumscribed about a rectangle if the difference between its sides is 4 and the perimeter is 56.

June 26, 2021 | education

| Area of a circle: S = П R², where R is the radius of the circle;

The radius of a circle circumscribed about a rectangle:

R = 1/2 √ (a² + b²), where a and b are the sides of the rectangle.

The perimeter of the rectangle is P = 2 * (a + b);

a – b = 4; a = b + 4; P = 2 * (b + 4 + b);

4 b + 8 = 56; 4 b = 48; b = 12; a = 12 + 4 = 16;

R = 1/2 √ (16² + 12²) = 1/2 √400 = 10;

S = P * 10² ≈ 314.

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