Question

The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

Answer 1

Here, the 2 similar equilateral triangle have Area scale factor 6, so linear scale factor root(6), so the length is 12*(1/root6)=2root6. I may be wrong.

Answer 2

Solve for x in: \[ \frac{\sqrt{3}} 4 \times (12)^2 = \frac{\sqrt{3}} 4 \times x^2 \times 6 \]

Answer 3

\(\implies x= 2\sqrt{6}\)

Answer 4

So, @henpen is right.

Answer 5

Area of the equilateral triangle of perimeter 36 is \( \frac{\sqrt{3}} 4 \times (12)^2 \)

Answer 6

Simmilary area of an equilateral triangle is given by \(\frac{\sqrt{3}} 4 \times x^2 \times 6\)

Answer 7

where x is the side length.