In a right triangle, the squares of the lengths of the two shorter sides (let's call them Square A and Square B) must add up to the square of the length of the hypotenuse (Square C). This is a consequence of the Pythagorean theorem.
Given:
- Area of Square A = 7 units²
- Area of Square B = 31 units²
To find the area of Square C (the hypotenuse), we use the equation:
\[ \text{Area of Square C} = \text{Area of Square A} + \text{Area of Square B} \]
Substituting the given areas:
\[ \text{Area of Square C} = 7 + 31 = 38 \]
Thus, the area of Square C is \( 38 \) units².