4.01: Area of a three-arc badge

0606/22/F/M/26 — Question 5 · 6 marks

The diagram shows a design for a badge. \(ABC\) is an equilateral triangle with side \(x\) cm. The arcs \(BC\), \(CA\) and \(AB\) are parts of the circles with centres \(A\), \(B\) and \(C\) respectively.

(a)

Write down the size of angle \(ABC\) in radians. Give your answer in terms of \(\pi\).

[1]

(b)

The area of the badge is \(2(\pi-\sqrt3)\text{ cm}^2\). Find \(x\).

[5]