The diagonal of the rectangle is 13 inches, and the side lengths of the triangles are pythagorean triples. to the nearest tenth, what is the area of the shaded part of the figure?

1) A Pythagorean triples is a set of three integers, a, b, c,  that follow the rule a^2 + b^2 = c^2

2) Assumin c is the diagonal of your rectangle and the hypotenuse of the triangles, you are looking this:

13^2 = a^2 + b^2

=> 169 = a^2 + b^2

Two integer numbers that meet that equality are 5 and 12:

5^2 = 25
12^2 = 144
=> 5^2 + 12^2 = 25 + 144 = 169

 => 13^2 = 5^2 + 12^2

Now that you have the three numbers you know the dimensions of the figure and can calculate the area of the shaded part. I cannot do that for you becasue you did not include the figure.