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Deepak Bora
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In the given figure, a square OPQR is inscribed in a quadrant OAQB of a circle. If the radius of circle is 6 √2 cm, find the area of the shaded region.

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CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number  – 30/5/1
Question Number –  34
square OPQR is inscribed in a quadrant
area of the shaded region
quadrant  of a circle

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1 Answer

  1. Given,
    Radius of circle r = 6 √2

    OA = OB = OQ =6 √2 cm

    In Δ OPQ,

    (OP)² + (PQ)² = (OQ)²

    2(OP)² = (6 √2)²

    a = op = 6 cm

    Area of the shaded region = ar (quadrant, with r = (6 √2) – ar (square with side 6 cm)

    = [1/4 (𝜋 × r²] − 𝑎²

    = [1/4 ( 3.14 × (6√2)² ) ] − 6²

    = [18 𝑥 3.14] − 36

    = 56.52 − 36

    = 20.52 cm²

    ∴ the area of the shaded region is 20.52 cm²

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