geometry

sri340 · Poincare Conjecture Offline Joined: 09 Jan 2008 Posts: 148

What percentage of the area of the trapezoid is the area of the
triangle?

please see the following pdf link problem no 13 (figure)

http://oame.on.ca/chapter/CHAMP/Contests/Grade%207/2007%20Grade%207.pdf

**Posted:** Tue Nov 03, 2009 3:39 am

isabella2296

First, let's find the area of the trapezoid. We can see from the figure that the bases are 10 and 5, and the height is 6. The area of any trapezoid is the average of the bases multiplied by the height (see if you can prove this!) Thus, the area is $7.5 \times 6 = 45$ .

Now for the area of the triangle. From the smaller base to the bottom vertex of the triangle, we see the length is 3. That means the height of the triangle is $6 - 3 = 3$ , and we can see the base is 10. Therefore, the area of the triangle is 15.

Ergo, the triangle takes up $\frac{15}{45} \approx 33\%$ .

**Posted:** Tue Nov 03, 2009 4:14 am

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