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  1. #1
    Member Rimas's Avatar
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    Triangle

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

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

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  3. #3
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    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.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ceasar_19134 View Post
    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
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