Question

Find the area of the polygon.

_12 cm

| 19 cm

12 cm

The area of the polygon is |

square centimeters.

Answer 1

`A = 1172.965\,cm^(2)`

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 =(360^(\textdegree))/(2\cdot \tan^(-1)\left((6\,cm)/(19\,cm) \right))`

`n = 10.271`

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

`\theta = (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 = (n\cdot l \cdot p)/(2)`

`A = ((10)\cdot (12.347\,cm)\cdot (19\,cm))/(2)`

`A = 1172.965\,cm^(2)`