Question

A round table cover has six equal designs as shown in figure. If radius of the cover is 15 cm and ABCDEF is a regular hexagon then find the total cost of making the shaded designs at the rate of Rs 10 per$\frac{44-21\sqrt{3}}{84}{cm}^2$.

Answer 1

R.E.F image

Area of shaded part

Area of circle - Area of triangles (total)

$=\pi r^2-6\frac{\sqrt{3}}{4}\times r^2$

$=(\frac{22}{7}-\frac{3\sqrt{3}}{2})(15{)}^{2}c{m}^2$

total cost $=\frac{(\frac{22}{7}-\frac{3\sqrt{3}}{2})\times {15}^2}{\frac{44-21\sqrt{3}}{84}}\times 10=\frac{\frac{44-21\sqrt{3}}{14}}{\frac{44-21\sqrt{3}}{84}}\times 10\times 15$

$=6\times 10\times 225$

$=Rs13500$