The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circum circle and the encircle of the triangle is $$\left( {{\text{use: }}\pi = \frac{{22}}{7}} \right)$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{Side of equilateral }}\Delta = 8{\text{ cm}} \cr & {\text{In circle radius}} = \frac{a}{{2\sqrt 3 }} = \frac{8}{{2\sqrt 3 }} = \frac{4}{{\sqrt 3 }} \cr & {\text{Circum radius}} = \frac{a}{{\sqrt 3 }} = \frac{8}{{\sqrt 3 }} \cr & {\text{Area bounded by both circle is}} \cr & = \pi \left\{ {{{\left( {\frac{8}{{\sqrt 3 }}} \right)}^2} - {{\left( {\frac{4}{{\sqrt 3 }}} \right)}^2}} \right\} \cr & = \frac{{22}}{7}\left( {\frac{{64}}{3} - \frac{{16}}{3}} \right) \cr & = \frac{{22}}{7}\left( {\frac{{48}}{3}} \right) \cr & = \frac{{22 \times 16}}{7} \cr & = 50\frac{2}{7}{\text{ c}}{{\text{m}}^2} \cr} $$