We know how to calculate the unknown sides and angles of right triangles using trigonometric ratios and the Pythagorean Theorem. We can use the same strategies to solve some problems with other shapes—for example, given a regular hexagon with side length 10 units, find its area.

Decompose the hexagon into 6 isosceles triangles. The angle at the center is 60 degrees because . That means we created 6 equilateral triangles because the base angles of isosceles triangles are congruent.

To find the area of the hexagon, we can find the area of each triangle. Drawing in the altitude to find the height of the triangle creates a right triangle, so we can use trigonometry. In an isosceles (and an equilateral) triangle, the altitude is also the angle bisector, so the angle is 30 degrees. That means , so  is about 8.7 units. The area of one triangle is about , or 43.5, square units. So the area of the hexagon is 6 times that, or about 261 square units.