In the pythagorean theorem proof prove that the inner square

In the pythagorean theorem? proof prove that the inner square below is a square.

Solution

Area of yellow square = c^2

Area of four right angled triangle = 4(1/2)(a*b) = 2ab

Total area = c^2 + 2ab

Using pythgorean theorem on right angled triangle : c^2 = a^2 +b^2

So, Total area = a^2 +b^2 + 2ab

= (a + b)^2

= (a+b)*(a+b)

Area of a square with sides (a+b)