Answer to Question #154090 in Geometry for Janine Leodones

Question

The perimeter of a regular polygon is 48 cm and its apothem is 6 cm. What is the area of the polygon?

Answer 1

The perimeter of a regular polygon is 48cm => P = 48cm and apothem is 6 cm => r = 6cm;

The formula of Regular polygon Circumscribing a circle is:

$Perimeter = 2nrtan(\frac{180^o}{n})$ and $Area = nr^2tan(\frac{180^o}{n})$

In the perimeter formula, see that $tan(\frac{180^o}{n}) = \frac{Peimeter}{2 * nr},$ substitute it to the Area:

$Area = nr^2*(\frac{P}{2*nr}) = \frac{1}{2}Pr = \frac{1}{2}*48*6 = 144cm^2$

Answer, Area = 144cm²