Area of the red triangle?

A hard-level "Area" problem.It works wherever the point is, and whatever shape the rectangle has.

Hints

Taking the four triangles one at a time gets you nowhere. The trick is to look at opposite pairs — blue with blue, orange with orange.
Draw one line through the point, parallel to the horizontal sides. The rectangle splits into an upper and a lower part. Look at the upper one (blue outline) first.
Compare the upper triangle with the upper rectangle. The base is the rectangle's width and the height is its height — exactly the same.
A triangle is base × height ÷ 2; a rectangle is base × height. So the upper triangle is exactly half of the upper rectangle.
The lower one is half of the lower rectangle for exactly the same reason.
Half of the upper rectangle plus half of the lower one makes half of the whole rectangle. So 13 + 17 is half the rectangle.
Now cut it vertically. For exactly the same reason, left and right are each half of their rectangle, so left + right is also half the rectangle.
Both are "half the rectangle", which means the two are equal.
13 + 17 = 30. Now just compute 30 − 19.

Answer 11cm²