Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 3.7 AMC 10/12 Find the answer United States

Problem:
A square and a regular hexagon are drawn with the same side length. If the area of the square is $\sqrt{3}$ , what is the area of the hexagon?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
The hexagon is composed of six equilateral triangles each of side length $\sqrt[4]{3}$ (with base $b = \sqrt[4]{3}$ and height $\frac{\sqrt{3}}{2} b$ ), so the total area is $\frac{9}{2}$ .

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