A square and a regular hexagon have the same perimeter. If the area of the square is 2.25, what is the area of the hexagon?
The sides of the square are , so the perimeter of the square is 4(1.5) = 6.
So the hexagon, which also has perimeter 6, will have sides of length 1.
To find the area of a regular hexagon, break it into 6 equilateral triangles:
Each of those can further be broken into 30º-60º-90º triangles, because all the angles in an equilateral triangle are 60º.
It’s easy enough to calculate the area of each of those: