A 3 by 3 grid of squares has one diagonal drawn in its centre square. How many quadrilaterals (four-sided figures) are there in the figure?

Rectangles: choose 2 of the 4 upright and 2 of the 4 flat lines, $\left(\genfrac{}{}{0ex}{}{4}{2}\right)\times \left(\genfrac{}{}{0ex}{}{4}{2}\right)=36$. The diagonal adds 4 trapeziums, each made of half the centre square and one neighbouring square (above, below, left or right). Total $36+4=40$.