b Now, we will find the area of the smaller square A_S.
Since the side length of the smaller square is c, the area of the square will be equal to c squared.
A_S=s^2 ⇒ A_S= c^2
c We will find the area of each triangle in terms of a and b. Notice that each triangle has a right angle where the sides of the square meet. All three triangles also have the same side lengths a, b, and c. Let's call the area of one of them A_T.
Remember that the area of a triangle is half the product of its base and its height. In a right triangle, if a leg is considered as a base, then the other leg becomes its corresponding height. With this information, we can write the area A_T of a right triangle with the legs a and b.
A_T=1/2bh ⇒ A_T=1/2 ab
d We know that the area of the larger square can be thought of as the sum of the area of the smaller square and areas of the four triangles. We will now write this equation algebraically.
A_L=A_S+A_T+A_T+A_T+A_T [0.5em] ⇕ [0.5em] A_L=A_S+4A_T
Let's substitute A_L= a^2+2ab+b^2, A_S= c^2, and A_T= 12ab into the equation and then simplify.
