ABCD is a square of side 12 cm. P, Q, R and S are the midpoints of the sides AB, BC, CD and AD respectively. Semicircles with PB, QC, RD and SA as diameters are drawn in the square. a. What is the area of the square? b. What is the total area of the semicircles? c. What is the area of the shaded portion?
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Step-by-step explanation:
We know that : Area of a Square is given by : Side × Side
Given : The Side of the Square as : 12 cm
→ Area of the given Square is : 12 × 12 = 144 cm²
Given : P , Q , R and S are the Midpoints of Sides AB - BC - CD - AD
→ Diameter of the Semi-Circles in Square is Half of the Side of the Square
→ Diameter of the Semi-Circle = 6 cm
→ Radius of the Semi-Circle = 3 cm
We know that : Area of Semi-Circle is given by : [πr²/2]
→ Area of Semi-Circle : [(3.14 × (9/2)] = 14.13cm²
As there are 4 Semi-Circles :
→ The Total Area of the Semi-Circles = (4 × 14.13) = 56.52 cm²
We can Notice from the Diagram, Area of Shaded Portion will be :
→ Area of Square - Area of 4 Semi-Circles
→ Area of Shaded Portion : (144 - 56.52) = 87.48 cm
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