Question

Centred at each corner of a regular hexagon, a part of a circle is drawn and a figure is cut out as shown below:

What is the area of this figure?

Answer 1

The area of the cut down portion = Area of the regular hexagon – Area of 6 sectors

Area of the regular hexagon

Area of the sector = 120°/360° part of area of the circle

(One angle of a regular hexagon is 120°)

Area of the 6 sectors = \(\frac{6\times \pi}{3}=2\pi\) cm²

Area of cut down portion = 6 √3 – 2 π cm²