Mathematics

In the figure (ii) given below, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. (π = 3.14)

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Given, length of each side of square = 20 cm.

We know that,

Length of diagonal of a square = $\sqrt{2}$ side = $20\sqrt{2}$ cm.

∴ OB = $20\sqrt{2}$ cm.

From figure,

OB is the radius of the quadrant OPBQ.

Area of quadrant OPBQ = $\dfrac{1}{4}πr^2$

$= \dfrac{1}{4} \times 3.14 \times 20\sqrt{2} \times 20\sqrt{2} \\[1em] = 3.14 \times 200 \\[1em] = 628 \text{ cm}^2.$

Area of square OABC = (side)²

= (20)² = 400 cm².

Area of shaded region = Area of quadrant OPBQ - Area of square OABC

= 628 - 400

= 228 cm².

Hence, area of shaded region = 228 cm².

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