39

In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. IF OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

Given:

OA = Side of square OABC = 20 cm

∵ Area of square = Side × Side

∴ Area of square OABC = 20 × 20 = 400 cm^{2}

Now,

∵ Length of diagonal of square = √2 × Side of Square

∴ Length of diagonal of square OABC = √2 × 20 = 20√2 cm

⇒ Radius of the quadrant = 20√2 cm

∵ Area of quadrant = πr^{2}

∴ Area of quadrant OPBQ = × 3.14 × 20√2 × 20√2

= × 400 × 2

= 3.14 × 200 = 628 cm^{2}

Area of shaded region = Area of quadrant OPBQ – Area of square OABC = 628 – 400 = 228 cm^{2}

__Hence, the area of the shaded region is 228 cm ^{2}.__

39

40

In the given figure, APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.

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