Answer:
144 cm²
Step-by-step explanation:
Finding square STUV's side lengths:
Square the area of square STUV to find the side lengths.
√169 = 13
Therefore, the side lengths of square STUV are 13 cm.
Finding triangle VRS last side length:
Since we now have 2 out of 3 side lengths for triangle VRS and it's a right triangle, we can use Pythagorean Theorem to find the last leg.
a² + b² = c²
a² + 5² = 13²
a² + 25 = 169
a² = 144
√a² = √144
a = 12
Therefore, the last side length is 12 cm.
Square PQRV's area:
Now that we know the side length of square PQRV is 12 cm, simply square the value to find the area.
12² = 144
Therefore, the area of square PQRV is 144 cm².
