The four coloured pieces in the image below can be put together in two different ways to make these shapes with base 13 units and height 5 units. Why is there one square missing in the second arrangement?
Neither of the \(13 \times 5\) “triangles” is a true triangle, because what appears to be the hypotenuse is bent. In the first “triangle” the hypotenuse bends inwards, and in the second it bends outwards.
Specifically, the blue triangle in the image has a slope of \(\frac{2}{5} = 0.4\) while the red triangle has a slope of \(\frac{3}{8} = 0.375\). This discrepancy accounts for the extra square.