Answer:
[tex]A = 1172.965\,cm^{2}[/tex]
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:
[tex]n =\frac{360^{\textdegree}}{2\cdot \tan^{-1}\left(\frac{6\,cm}{19\,cm} \right)}[/tex]
[tex]n = 10.271[/tex]
The polygon has ten sides and the side length shall be re-adjusted:
[tex]\theta = \frac{360^{\textdegree}}{10}[/tex]
[tex]\theta = 36^{\textdegree}[/tex]
The side length is:
[tex]l = 2\cdot (19\,cm)\cdot \tan 18^{\textdegree}[/tex]
[tex]l = 12.347\,cm[/tex]
The area of the polygon is:
[tex]A = \frac{n\cdot l \cdot p}{2}[/tex]
[tex]A = \frac{(10)\cdot (12.347\,cm)\cdot (19\,cm)}{2}[/tex]
[tex]A = 1172.965\,cm^{2}[/tex]
