Question

Find the area of a regular hexagon with the given measurement.

48-inch perimeter

A = sq. in.

whoever gets this right gets MEDALS!!!!

Answer 1

Because the perimeter is 48 and each side is of equal length (because the hexagon is regular), the length of is side is\[\frac{48}{6} = 8.\]Now, if you draw the diagonals of a regular hexagon you get six equilateral triangles, and the sides of any of these equilateral triangles is 8. The area of one of this triangles is\[\frac{8 \cdot \sqrt{8^2 - 4^2}}{2} = 4\sqrt{64-16} = 16\sqrt{3}\]and because there are six triangles the total areaof the hexagon is\[6 \cdot 16\sqrt{3} = 96\sqrt{3}.\]