First, we need to find the area of the trapezoid by using the area formula
of the trapezoid.
A=(1/2)h(b1+b2) area of a trapezoid
In the above diagram, h=a+b, b1=a, and b2=b.
Now, let's find the area of the trapezoid by summing the area of the three right triangles.
The area of the yellow triangle is
The area of the red triangle is
The area of the blue triangle is
The sum of the area of the triangles is
1/2(ba) + 1/2(c^2) + 1/2(ab) = 1/2(ba + c^2 + ab) = 1/2(2ab + c^2).
Since, this area is equal to the area of the trapezoid we have the following relation:
(1/2)(a^2 + 2ab + b^2) = (1/2)(2ab + c^2).
Multiplying both sides by 2 and subtracting 2ab from both sides we get