A small square is placed inside a big square. The vertices of the small square are joined to vertices of the large square so as to divide the region between the squares into four quadrilaterals, with areas, in order, a, b, c, d.
Prove that a+c=b+d.

Now, each pair of opposite trapeziums could be fitted together, with their slant edges coinciding, to form a rectangle with width p and length L – p, where p is the projection of WX on AB (same for all other pairs) and L is the length of a side of the large square.

Thus[T_{a} + T_{c}] = [T_{b} + T_{d}],and (1) now gives[a + c] – [b + d] = 0 and