If two equilateral triangles of area A intersect to form a regular hexagon then what is the area of the hexagon?

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- Oct 24th 2006, 02:56 PMRimasTriangle
If two equilateral triangles of area A intersect to form a regular hexagon then what is the area of the hexagon?

- Oct 24th 2006, 09:35 PMSoroban
Hello, Rimas!

An interesting problem . . . Did you make a sketch?

Quote:

If two equilateral triangles of area A intersect to form a regular hexagon,

then what is the area of the hexagon?

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Each equilateral triangle is comprised of nine smaller triangles.

They overlap in a hexagon comprised of six triangles.

The hexagon has an area which is $\displaystyle \frac{6}{9} = \frac{2}{3}$ of an equilateral triangle.

Area of hexagon: .$\displaystyle \frac{2}{3}A$

- Oct 27th 2006, 08:09 AMceasar_19134
Just looking around, but shouldnt the Area of the hexagon only equal 1/2 of the figure?

The hexagon is composed of 6 triangles, while the whole figure is composed of 12. - Oct 27th 2006, 08:48 AMCaptainBlack