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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)

In the figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Mensuration

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Answer

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

In the figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

We know that,

Length of diagonal of a square = 2\sqrt{2} side = 20220\sqrt{2} cm.

∴ OB = 20220\sqrt{2} cm.

From figure,

OB is the radius of the quadrant OPBQ.

Area of quadrant OPBQ = 14πr2\dfrac{1}{4}πr^2

=14×3.14×202×202=3.14×200=628 cm2.= \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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