Geometry find area of triangle with no measurements

Question

We have a triangle inside a square which has four smaller squares. The base of the triangle divides one of the smaller squares in half. The tip of the triangle is one corner of the bigger square. Without knowing the measurements, how can we discover which fraction of the big square is comprised of the triangle?

Answer 1

A possible sketch of the triangle.

It has base $\displaystyle \frac{1}{2}s$ and height $\displaystyle \frac{3}{4}s$, and thus has area $\displaystyle \frac{3}{16}s^2$.

The ratio of the triangle's area to the square's area is $\displaystyle \frac{\frac{3}{16}s^2}{s^2}=\frac{3}{16}$

Therefore, $\displaystyle \boxed{\frac{3}{16}}$ of the square is comprised of the triangle.