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I have an equilateral triangle and I put another equilateral triangle within it. The inner triangle has exactly half of the area of the outer triangle. As well, the inner triangle is placed in the centre of the outer triangle i.e. they both have the same central point.

I want to measure the distance from one side of the inner triangle to the same side of the outer triangle.

My thinking is like so:

To find this distance, all i need is the apothem of the larger triangle minus the apothem of the smaller (inner) triangle.

What do you think?

I also calculated this to be: ( 1 - (1/sqrt(2)) ) * ( outer triangle apothem )

Do people get the same result as me? Or did I do something wrong? or make a bad assumption?

please help.

thanks