Question

Four equal circles, each of radius a, touch each other. Show that the area between them is 6/7a 2

Answer 1

the aswer is given in the photo 
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Answer 2

Answer:

Area of the shaded region = 6a²/7

Step-by-step explanation:

Draw four equal circle in which

Let A,B,C, D center of the given circle,

join all the center in a sequence to form square, ABCD is a square of side 2a.

Area of Square ABCD = (2a)² = 4a² unit²

The Area of Shaded Region = Ar(Sq. ABCD) - 4* Ar of Sector

                                               =  4a² - 4*(1/4)*π r²

                                               = 4a² - π r²

                                                = 4a² - 22/7*a²

                                                = (28a²- 22a²)/7

                                                = 6a²/7

Area of the shaded region = 6a²/7.