The figure above shows three consecutive squares of sides 5, 4 and 3, respectively.
Find the area of the black region.
Extend the side of 3 x 3 square 2 units up and draw a straight line to the left to connect it to the right corner of 5 x 5 square. Now, you have a rectangle with sides 5 x [5 + 4 +3] = 5 x 12 =60 sq. units. Half of it is 60/2 =30 sq units, which is the area of the white right triangle with 5, 4, 3 units at the bottom. But the area of the 3 squares is:[3 x 3] + [4 x 4] + [5 x 5] =50 sq. units. So, the black area =50 - 30[The area of right triangle] =20 sq. units.
