Question

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35 cm then find the total area of the design. [ Use $\sqrt{3}1.732and\pi =3.14$]

Answer 1

Join each vertex of the hexagon to the centre of the circle.

The hexagon is made up of six triangles.

The total area of the design = Area of the circle - Area of six triangles

$=[\frac{22}{7}\times 35\times 35]-[6\times (\frac{\sqrt{3}}{4}\times 35\times 35\left)\right]$

$=(35\times 35)[\frac{22}{7}-(6\times \frac{1.732}{4}\left)\right]$

$=1225(\frac{22}{7}-2.598)$

$=1225\times 0.542$

$=663.95c{m}^2$