### Home > GC > Chapter 8 > Lesson 8.3.2 > Problem8-100

8-100.

A regular hexagon with side length $4$ has the same area as a square. What is the length of the side of the square? Explain how you know.

If a polygon is regular with $n$ sides, it can be subdivided into $n$ congruent isosceles triangles. One way to calculate the area of a regular polygon is to multiply the area of one isosceles triangle by $n$.

The area of a square is $\text{A}=s^2$. So to determine the side length of the square take the square root of the hexagon's area (since they are equal).