In the given figure, ABCD is a square of side 14 cm. With centers A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Asked by Pragya Singh | 1 year ago |  60

1 Answer

Solution :-

Side of square = 14 cm

Four quadrants are included in the four sides of the square.

Radius of the circles = \( \dfrac{14}{2}\) cm = 7 cm

Area of the square ABCD = 14= 196 cm2

Area of the quadrant = \( \dfrac{πR^2}{4} \) cm2 = (\( \dfrac{22}{7}\)) ×\( \dfrac{7^2}{4}\) cm2

\( \dfrac{77}{2}\) cm2

Total area of the quadrant = 4×\( \dfrac{77}{2}\) cm= 154cm2

Area of the shaded region = Area of the square ABCD – Area of the quadrant

= 196 cm– 154 cm2

= 42 cm2

Answered by Abhisek | 1 year ago

Related Questions

Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).
 

Class 10 Maths Areas Related to Circles View Answer

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
 

Class 10 Maths Areas Related to Circles View Answer

The outer circumference of a circular race-track is 528 m. The track is every­where 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre 
 

Class 10 Maths Areas Related to Circles View Answer

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

Class 10 Maths Areas Related to Circles View Answer

A path of width 3.5 m runs around a semi­circular grassy plot whose perimeter is 72 m. Find the area of the path.

Class 10 Maths Areas Related to Circles View Answer