Two Congruent Circles

The area of one of these circles is $3.14$ x $r^{2} = 10$
$r^{2} = \frac{10}{3.14}$
The area of the rectangle is $2r$ x $3r = 6r^{2}$
$= 6$ x $\frac{10}{3.14} = 19.108 = 19$

Just a suggestion for further problems like this. It's better if you put, "the area can be expressed as $\dfrac{a}{\pi}$ where a is a positive integer. What is the value of a." It just a small change that eliminates the use of a calculator and helps improve your problems. But over all, great problem, quite original.

area of circle= 22/7r^2=10 r^2=70/22

since the distance between the centers and the center from the border is the radius, the length of rectangle comes out to be 3r.

the breadth is same as the diameter i.e. 2r.

area of rectangle=2r * 3r = 6r^2 = 6* 70/22 =19 (approx.)

The rectangle can be divided into six squares, each having area equal to R^2.

area of circle =3.14r^2 => 10=3.14r^2 => 10/3.14=r^2 => r=1.78 length of rectangle=3r width of rectangle=2r area of rectangle= 3r * 2r = (5.35*3.569) =19.094= 19

area of circle =3.14r^2 => 10=3.14r^2 => 10/3.14=r^2 => r=1.78

length of rectangle=3r
width of rectangle=2r

area of rectangle= 3r * 2r
= (5.35*3.569) =19.094= 19

r=undr(10/pi);(3r*2r)=19.09859317

Pi.RSquare=10 units,Area of rectangle is L*b,Since the circle covers the breadth of rectangle,breadth =2r ,and since each one touches one end of the length of rectangle and passes through the centre of the other circle,the length is 2r+2r-r(the shared portion).

Hence l=3r,b=2r, Area of rectangle =6 r r,we have Pi.r r=10,hence area of rectangle =6 r r=6 10/Pi=60/Pi=60/22/7=60*7/22=19 roughly.