Q11 of 52 Page 160

In the figure 7.48, square ABCD is inscribed in the sector A- PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region.

Side of square ABCD = radius of sector C - BXD = 20 cm


Area of square = (side)2 = 2002 = 400 sq.cm


Area of shaded region inside the square = Area of square ABCD - Area of sector C - BXD





⇒ 76 sq.cm


Radius of bigger sector = Length of diagonal of square ABCD



Area of the shaded regions outside the square = Area of sector A - PCQ - Area of square ABCD = A(A - PCQ) - A(ABCD)




⇒ 628 – 400


⇒ 228 sq.cm


∴ total area of the shaded region = 86 + 228 = 314 sq.cm.


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