Q13 of 35 Page 311

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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