Q. 133.8( 11 Votes )

# 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.

Answer :

**NOTE:** Area of square = (side)^{2}

Area of circle = πr^{2}, 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)

AB^{2} + BC^{2} = AC^{2}

⇒ x^{2} + x^{2} = 14^{2}

⇒ 2 x^{2} = 196

⇒ x^{2} = 98

⇒ Area of square = x^{2} = 98cm^{2}

Area of circle = πr^{2} where r is the radius of the circle

=

⇒ Area of circle = 154 cm^{2}

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

= 154 – 98 cm^{2}

= 56 cm^{2}

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}

= 7^{2} = 49 cm^{2}

Area of each circle = π r^{2}, where r is the radius of circle

=

Area of four circle = 4× area of each circle

= 4 × 38.5 = 154 cm^{2}

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

= 154 – 49 cm^{2}

= 105 cm^{2}

Rate this question :

The inner diameter and external diameter of an Iron ring plate are 20 cm and 22 cm. The quality of iron plate in the ring is

West Bengal MathematicsThe ratio of the area of an equilateral triangle inscribing a circle is

West Bengal Mathematics