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

Deepak BoraNewbie

# 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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This answer was edited.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