## What’s the number of Triangles in irregular hexagon ?

June 1, 2017 § Leave a comment

Hello Everyone 🙂

we have this hexagon with sides’ lengths from top to right 1,2,1,2,1,2 cm respectively, and hope to find what’s exactly how many triangles can be formed in this irregular hexagon ?

**First:**we’ll join three small regular triangles to sides

*a*

_{1,}

*a*

_{3, }

*a*

_{5}= 1, 1, 1 respectively of the hexagon. then we have a big one triangle.

**Second:**if we add

*a*

_{1}to

*a*

_{2}to

*a*

_{3}then we get the length of one side of the big triangle and the remaining equal it.

**Third:**then we can say that the hexagon area = (

*a*

_{1}+

*a*

_{2}+

*a*

_{3})

^{2}-

*a*

_{1}

^{2}-

*a*

_{3}

^{2}-

*a*

_{5}

^{2 }

if we considered that the length of one small triangle equal to 1 and consider the big triangle have sides of X cm then we have area

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