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# I just want to share a rule about the triangle. I hope most

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Director
Joined: 14 Jan 2007
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I just want to share a rule about the triangle. I hope most [#permalink]  29 May 2007, 09:54
I just want to share a rule about the triangle. I hope most of you already know about it.

The area of the triangle, which has the midpoints of the sides of some triangle x as vertices is the one fourth of the area of triangle x.

Proof:
Say the big triangle is - triangle x
small triangle is - triangle y

the area of the triangle x = sqrt[s(s-a)(s-b)(s-c)] where s = semi perimeter of the triangle x = (a+b+c)/2
semi perimeter of triangle y will be s/2
so area of the small triangle = 1/4 of the area of triangle x

Hope it helps.
Manager
Joined: 13 Feb 2007
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the formula used above is heron's formula, no?
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