### Home > INT2 > Chapter 8 > Lesson 8.4.1 > Problem8-84

8-84.

An exterior angle of a regular polygon measures $18°$.

1. How many sides does the polygon have?

Remember that the sum of all exterior angles is equal to $360°$.

2. If the length of a side of the polygon is $2$ units, what is the area of the polygon?

Find the central angle. Make an isosceles triangle with the central angle and the given side length.  Create 2 right triangles from the isosceles triangle. Use right angle trigonometry to calculate the area of one of the two right triangles.  Then multiply that by the number of congruent right triangles within the polygon.  Check the math notes for more information.

$\approx126.3 \; \text{units}^2$