Below is an equilateral hexagon.
AB = 7
FC = 14
AE = 12.124
What is the area of the hexagon?
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Below is an equilateral hexagon.
AB = 7
FC = 14
AE = 12.124
What is the area of the hexagon?
The hexagon consists of two equal trapezoids, so we will strive to calculate the area of one of them and multiply it.
AFE is an isosceles triangle,
its height (FG) crosses the base exactly in the center, therefore:
We replace and discover:
We replace the data in the formula for the area of a trapezoid:
63 is the area of half of the hexagon, therefore:
127.3
Given the following trapezoid:
Calculate the area of the trapezoid ABCD.
A regular hexagon has a vertical line of symmetry through its center. This line divides it into two identical trapezoids that share the same dimensions, making calculation easier!
The trapezoid height is the perpendicular distance from one parallel base to the other. Since AE = 12.124 is the full hexagon height, each trapezoid has height = .
The two parallel sides are AB = 7 (top base) and the middle section FC = 14 (bottom base). These form the parallel edges of each trapezoid.
You calculated the area of one trapezoid, but the hexagon contains two identical trapezoids. So: Total Area = 2 × (One Trapezoid Area).
The standard formula only works for regular hexagons where all sides are equal. This hexagon has different side lengths, so use the trapezoid method!
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