Thread: Triangle

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

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?

Code:

                *
               / \
          *---*---*---*
           \ /o\o/o\ /
            * - * - *
           / \o/o\o/ \
          *---*---*---*
               \ /
                *

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 of an equilateral triangle.

Area of hexagon: .

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.

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