# Thread: Find Area of ∆ABC

1. ## Find Area of ∆ABC

If the area of square ABCD is 36, what is the area of
∆ABC which lies inside square ABCD?

NOTE:

Point Q(2,5) lies on CD of square ABCD.

Point P(6,9) lies on BC on square ABCD.

Point A of ∆ABC coincides with point A of square ABCD.

I determined the area to be 21 but the text book tells me that the answer is 16.

What did I do wrong?

I hope this information is clearly stated here.

Thanks

2. Are you sure it's $\displaystyle \triangle ABC$ you need to find the size of, not $\displaystyle \triangle APQ$?

If so, we haven't got enough information about where A is, unless the square is positioned so the sides are horizontal and vertical.

If this is the case, then C is at point (2, 9), which means A is at (8, 3) (6 over from C and 6 down - you know it's 6 because the square is area 36.

So you need to find the area of the triangle (2,5), (6,9), (8,3).

Can you take it from there?

3. ## Yes..

Originally Posted by Matt Westwood
Are you sure it's $\displaystyle \triangle ABC$ you need to find the size of, not $\displaystyle \triangle APQ$?

If so, we haven't got enough information about where A is, unless the square is positioned so the sides are horizontal and vertical.

If this is the case, then C is at point (2, 9), which means A is at (8, 3) (6 over from C and 6 down - you know it's 6 because the square is area 36.

So you need to find the area of the triangle (2,5), (6,9), (8,3).

Can you take it from there?

Yes, I need to find the area of ∆APQ. Can you show me?

4. Find the areas of the triangles you've got left and subtract those from the big square. They're easy right-angled triangles and should be no problem.