We have three squares, which sides are the same of a square triangle.
We know the area of 2 out of the 3 squares. We have to find the area of the third.
The area of the smaller square is 81. As b it is side, the area of the square is b^2=81.
The area of the biggest triangle is c^2=369.
The area we need to find has a value of a^2.
As we have a square triangle, we can apply the Pythagorean theorem:
[tex]a^2+b^2=c^2^{}[/tex]
As we already know the values of b^2 and c^2, we can find the area of the square as:
[tex]\text{Area}=a^2=c^2-b^2=369-81=288[/tex]
Answer: the area of the square is a^2=288.
