A graphic designer is creating a logo that includes a 'shard' element. This shard is defined as the segment of a circle with centre C C\,C and radius 43 cm4\sqrt{3}\text{ cm}43 cm. The segment is bounded by the chord PQ PQ\,PQ and the arc PQPQPQ, where the angle subtended at the centre, ∠PCQ\angle PCQ∠PCQ, is π3\displaystyle \frac{\pi}{3}3π radians.
Show that the area of the shard is
k(2π−33) cm2 k(2\pi - 3\sqrt{3})\text{ cm}^2 k(2π−33) cm2where k k\,k is an integer to be found.
