Question

I will send you a picture of the work problem and the answer choices

Answer 1

Area of a triangle (At):

$A_t=\frac{b\times h}{2}$

In your problem:

b = b

h = a

As you have four triangles in the figure:

$A_t=4\times\frac{b\times a}{2}=2ab$

Area of a square (As):

$A_s=c^2$

The expression of the area (A) of the figure would be:

$A=2ab+c^2$$A\text{ =(}a+b)^2$

Also, solving the quadratic expression, the equivalent would be:

$A\text{ =}a^2+2ab+b^2$

Setting two of these equal to each other and subtracting 2ab from the equation results in the Pythagorean Theorem

$\begin{gathered} 2ab+c^2\text{ =}a^2+2ab+b^2 \\ -2ab+2ab+c^2=a^2+2ab-2ab+b^2 \\ c^2=a^2+b^2 \end{gathered}$