Answer:
43
Step-by-step explanation:
The sides of the squares make up the sides of the triangle.
To find the measure of a side of the square, take the area given and square root it, since the area of a square is equal to the length of its side squared.
For the 9cm^2 area, the square root of 9 is 3, so each side is 3 cm.
For the 34 cm^2 area, the square root of 34 is about 5.83, so each side is about 5.83 cm.
Plug these into the Pythagorean theorem ([tex]a^2+b^2=c^2[/tex]) for a and b.
You get [tex]9+34=c^2[/tex].
Solve for c by square rooting both sides to get about 6.56.
Since it's asking for the area, square 6.56 to get 43.
An easier way to do this would be to recognize that [tex]a^2[/tex], [tex]b^2[/tex], and [tex]c^2[/tex] are all equal to the area of their respective squares, since the area of a square is equal to its side squared, and the Pythagorean theorem is also squaring the sides.
Using this information, a^2 is 9, b^2 is 34.
Once you add them up, you get c^2, and you know that c^2 is the area of the square the question is asking for.
Therefore, c^2 is equal to 9 + 34, or 43.
