Finding area common to two circles

Question

Having trouble finding the area common to the two mats.

The correct answer is $99.1cm^2$

Answer 1

Hope, it helps. I used Law of cosine and segments area formula.

Answer 2

I can help you think how to solve this question leaving the calculation part for you.

1. Since we know that the line joining the two centres is bisected (divided into two equal parts), as same radius, by the common chord. From here we can easily calculate length of the common chord using the Pythagoras Theorem.(p=radius of circle, b=half of chord, h=half of distance between two centres)
2. We can easily find area of the sector marked by the arc between the ends of the common chord and the radii at the two ends (lets name it area1). But first we have to find the angle subtended by that arc. It is 2cos^-1(h/r). (lets name it s). According to formula - area1={s/(2pie)}*r (note that s is in radians and pie=3.14). We can also find the area of the triangle formed by the common chord and the two radii at their ends. (lets name it area2). area2=hxb. Area common to the two mats is simply 2x(area1-area2).