Question

Find the area of the polygon.

Answer 1

Answer:

$A = 1172.965\,cm^{2}$

Step-by-step explanation:

Let be a side of 12 cm (l) and an apothem of 19 cm (p). First, the number of sides has to be determined:

$n =\frac{360^{\textdegree}}{2\cdot \tan^{-1}\left(\frac{6\,cm}{19\,cm} \right)}$

$n = 10.271$

The polygon has ten sides and the side length shall be re-adjusted:

$\theta = \frac{360^{\textdegree}}{10}$

$\theta = 36^{\textdegree}$

The side length is:

$l = 2\cdot (19\,cm)\cdot \tan 18^{\textdegree}$

$l = 12.347\,cm$

The area of the polygon is:

$A = \frac{n\cdot l \cdot p}{2}$

$A = \frac{(10)\cdot (12.347\,cm)\cdot (19\,cm)}{2}$

$A = 1172.965\,cm^{2}$