A square is a quadrilateral whose four angles are all right angles and whose all sides are equal.

Let be a square with each side in length equal to and is a diagonal which divides the square into two equal triangles, and. Since, is a right triangle. Therefore

Similarly,

__Example__:

A chess board contains equal squares and the area of each square is square cm. a border round the board is cm wide. Find the length of the side of chess board.

__Solution__:

There are equal squares each of area square cm.

Total area bounded by squares square cm

One side of the square containing small squares cm

Width of the border cm

Length of side of chess board cm.