What is the perimeter of hexagon whose area is 24?

Answer 1

A regular hexagon is made up of six congruent equilateral triangles, the area of an equilateral triangle can be computed using the formula s2(√3)/4, where s is the length of one side of the triangle. Since the hexagon comprises 6 equilateral triangles, each triangle has an area of 24/6 = 4. Solving for 4 = s2(√3)/4 gives s = 4/(3^(1/4)). Since one side of the triangle is also one side of the hexagon, we can multiply this by 6 to find the perimeter of the hexagon: 6 × 4/(3^(1/4)) = 8×3^(3/4) ≈ 18.23

Therefore, the perimeter of a hexagon whose area is 24 is

8×3^(3/4)

or approximately 18.236056455638221135948506015709