Question

Can you finds the numbers of sides in a polygon if measure of each side is $7cm$, its apothem is $4cm$ and the area of polygon is $112c{m}^2$

Answer 1

Let the polygon will be regular polygon, so the polygon can be divides into equilateral triangle.

Here, side and apothem is given means base and height are given.

$\Rightarrow$ Area of equilateral triangle $=\frac{1}{2}\times base\times height.$

$=\frac{1}{2}\times 7\times 4$

$=14c{m}^2$

$\Rightarrow$ Area of polygon $=112c{m}^2$

$\Rightarrow$ Number of sides of polygon $=\frac{112c{m}^2}{14c{m}^2}=8$

$\therefore$ Number of sides of polygon is $8$