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 Triangle Donut (Posted on 2006-01-01)
If X is the area of any triangle-PQR and you make a hole in the center of this triangle by first joining the midpoints of each side to create smaller triangle-STU and then again joining the midpoints of triangle-STU to create the hole in the center of this triangle, it would create a donut something like this:
```          Q
/ \
/   \
/     \
S /_______\ U
/ \  A  / \
/   \/_\/   \
/     \ /     \
P /_______V_______\ R
T
```
What is the area of the triangle donut in terms of X?

 See The Solution Submitted by tanx Rating: 3.0000 (1 votes)

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 The solution | Comment 1 of 14

Since S,T,U are the mid points of ¥ÄPQR so ST = ¨öQR and          UT = ¨öPQ and SU = ¨öPR and all sides ST, TU, US are parellel to RQ, QP and PR respectively.

Therefore area of ¥ÄSTU = ¨ù area of ¥ÄPQR

Let A be the mid-point of ST,B be the mid-point of TU,  and C be the mid-point of US.

SO similiarly as above

area of ¥ÄABC = ¨ù area of ¥ÄSTU

Therefore area of ¥ÄABC = (1/16)*X

and area of triangle donut  = (1/4)*X-(1/16)*X = (3/16)*X

 Posted by akash on 2006-01-01 11:16:26

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