# Let us write by calculating the area of shaded region pictures below.ABCD is a square. The length of radius of circle is 7 cm.The length of radius of each circle is 3.5 cm. The centres of four circles are A, B, C, D respectively.

NOTE: Area of square = (side)2

Area of circle = πr2, where ‘r’ is radius of the circle.

i) Given, ABCD is a square

The length of the radius of circle = 7 cm

Diameter of the circle = 14cm

Let the side of square ABCD = x cm

By Pythagoras theorem (being a square there is angle of 90° between two adjacent sides)

AB2 + BC2 = AC2

x2 + x2 = 142

2 x2 = 196

x2 = 98

Area of square = x2 = 98cm2

Area of circle = πr2 where r is the radius of the circle

=

Area of circle = 154 cm2

Area of shaded region = area of circle – area of square

= 154 – 98 cm2

= 56 cm2

ii) Given, Radius of each circle = 3.5cm

And A,B, C, D are center of each circle

Hence, ABCD forms a square with each side of 7cm length

Area of square = (side)2

= 72 = 49 cm2

Area of each circle = π r2, where r is the radius of circle

=

Area of four circle = 4× area of each circle

= 4 × 38.5 = 154 cm2

Area of shaded region = area of four circles – area of square

= 154 – 49 cm2

= 105 cm2

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