 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  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) Comments: ( Back to comment list | You must be logged in to post comments.) The solution | Comment 1 of 14

Since S,T,U are the mid points of ��PQR so ST = ��QR and          UT = ��PQ and SU = ��PR and all sides ST, TU, US are parellel to RQ, QP and PR respectively.

Therefore area of ��STU = �� area of ��PQR

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 ��ABC = �� area of ��STU

Therefore area of ��ABC = (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 Please log in:

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