How to Find the Area of This Composite Figure

Question

In my assignment, I have this problem that I must find the exact value for:

I'm not sure, but I think I should first draw another triangle above the 35 cm, making a rectangle. I could find the area of the rectangle (49 * 23). Then, I can do the Pythagorean Theorem for that other triangle (35^2+b^2=49^2 ---> b=sqrt 1176), subtracting the total from the rectangle area. But, to me, this method is not correct because there is a small triangle-shaped space near the 23 cm, so I'm not sure my finding of the area will work.

Step by step, could you explain how you would find the area of this composite?

Answer 1

If the length of the left-hand vertical line is also 23 cm, your answer is correct, since the line across the top completes a rectangle.

Otherwise, this is not a well-posed question. For example, imagine the left-hand vertical line being stretchable, and the two diagonal lines being glued together in a right angle. As the left-hand line stretches, you can maintain the right angle (possibly by changing the length of the unlabeled diagonal line), and the area clearly changes.

Answer 2

Fiddling around with geometry toys, I was able to make this:

Here, $AC,AD$ and $EF$ are fixed lengths, and angles $A,C$ and $E$ are fixed to be right angles. The lengths of $CF$ and $ED$ are derived by the program, and I guess are not exact.

The only problem I have, is that, when I drag $E$ so the angle becomes right, and $F$ and $D$ are at the same height, I get this:

So I am not so sure if the exercise is completely sensible.