Look carefully at the shapes on the left. There are two triangles with right angles in, and two other shapes, with two right angles each. The British would call these trapeziums as they have two sides parallel (apparently the Americans sometimes don't!) They fit together into a square 8 units on each side (as 5 + 3 = 8). That means that the square has area 8 x 8 = 64 square units.
Now look at the shape below. I have rearranged the same shapes in a different way, moving the triangles and rotating the trapeziums. The colours show which shape is which. The new shape is a rectangle with sides 5 units and 13 units (= 8 + 5). So the area of the rectangle is 5 x 13 = 65 square units. Wait a minute! We seem to have gained a square unit! Where did it come from?
Solution - but don't click here until you've tried it for yourself. The solution is more fun, and makes more sense, after your own attempts.
© Jo Edkins 2009 - Return to Puzzles index