Question

The area of a regular hexagon is {864 sqrt 3cm square}. Find the length of a side.

Answer 1

there is a formula for the area of a hexagon that relates area A to side length\[A=\frac{3\sqrt{3}}{2}x^2\]so in this case\[864\sqrt{3}=\frac{3\sqrt{3}}{2}x^2\]\[x^2=864\sqrt{3}*\frac{2}{3\sqrt{3}}=576\]finally, the side length in cm is\[x=\sqrt{576}=24\]

Answer 2

New question.
Corollary 7.5 shows the formula for the area of an equilateral triangle is Where s is the measure of the side of the triangle. Use A=1/2 ap to show the same formula is true for any equilateral triangle with sides.