In the adjoining figure, points P,Q,R,S, are centers of circle. radius of all circls are equal. Side of square PQRS is 14 cm. find the area of the shaded portion?
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Answer :-
Area of the shaded portion is 42 cm².
Given:-
- PQRS is a square of side 14 cm.
- Talking P, Q, R and S as centres four circles are drawn. (of same radius)
Find:-
Area of the shaded portion.
Solution:-
Area of square = (side)²
⇒ 14 × 14
⇒ 196 cm²
Now,
Diamter of each circle is 14 cm. Means, radius of circle is half of diameter.
So, radius of circle = 7 cm
Area of four quadrants of circle = 4 × Area of quadrant of circle
⇒ 4 × 1/4 × πr²
⇒ 4 × 1/4 × 22/7 × 7 × 7
⇒ 22 × 7
⇒ 154 cm²
Area of shaded region = Area of square - Area of four quadrants of circle
Substitute the known values above
⇒ (196 - 154) cm²
⇒ 42 cm²
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