Area of Square on Hexagon Diagonal

Question

Let $ABCDEF$ be a regular hexagon with each side of length $1	ext{ cm}$. The area (in sq cm) of a square with $AC$ as one side is

Accepted Answer

B. In regular hexagon $ABCDEF$, $AB = BC = 1	ext{ cm}$ and $\angle ABC = 120^\circ$. Using Law of Cosines in $	riangle ABC$: $$AC^2 = AB^2 + BC^2 - 2(AB)(BC)\cos(120^\circ)$$ $$AC^2 = 1^2 + 1^2 - 2(1)(1)\left(-\frac{1}{2}ight) = 1 + 1 + 1 = 3$$ Since $AC^2$ is the area of a square constructed on $AC$, the area is 3 sq cm.

Answer

$3\sqrt{2}$

Answer

3

Answer

4

Answer

$\sqrt{3}$

Area of Square on Hexagon Diagonal

Explanation

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