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a regular hexagon is like 6 isosceles triangles squashed together, with a 60 degree angle in the center of the hexagon (because 360 degrees / 6 = 60 degrees).

in this problem each of those triangles have two sides of length 24

area of an isosceles triangle (when we know the inside angle and the 2 sides) is:

A = (1/2) * side^2 * sin(angle)

A = 0.5 * 24^2 * sin(60)

A = 0.5 * 576 * sqrt(3)/2

A = 144 * sqrt(3)

but we have 6 triangles to make the hexagon, so

Answer = 864 * sqrt(3)
by Level 13 User (103k points)

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