Use a right triangle to construct a large square, as shown in the illustration below.

The length of any side of the large square is the sum of the lengths of the legs of the right triangle.

The length of any side of the small internal square is the length of the hypotenuse of the right triangle.

Calculate the area of the large square two different methods (as shown in the illustration below)

• Method one: Use the formula for the area of a square using the length of the side of the large square.
• Method two: Add the areas of the four triangles and the small internal square.

Equate the equivalent expressions from the two methods and simplify.