1. ## Triangle

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

2. Hello, Rimas!

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

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 $\frac{6}{9} = \frac{2}{3}$ of an equilateral triangle.

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

3. 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.

4. Originally Posted by ceasar_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.
The area of the hexagon is given in terms of the area of one of the
equilateral triangles, each of which is 9 of the small triangles compared to
six which comprise the hexagon.

RonL