Identify and Set Up
This question is a test on the understanding of the Pythagorean theorem.
It states that the square of the length of the hypothenuse of a right angled triangle is equal to a sum of the squares of the other sides.
Our approach, given the length of the other sides, is simply to find the square of the hypothenuse which is a sum of the square of the other 2 sides.
Execute

This gives us:
a.
![h^2=17^2+26^2=965\operatorname{cm}^2]()
Area of square with length as hypotenuse = 965 sq cm
b.
![h^2=7^2+15^2=274\operatorname{cm}]()
Area of square with length as hypotenuse = 274 sq cm