Question

Q.12) In the adjoining figure, points P, Q, R, S are centres of
a circles. Radii of all circles are equal. Side of square PORS
is 14 cm. Find the area of the shaded portion.
1) 32 sq. cm
2) 48 sq. cm
3) 56 sq. cm
4) 42 sq. cm
7.5 and its height is 14 cm​

Answer 1

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Step-by-step explanation:

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Answer 2

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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