A right triangle has non-hypotenuse side lengths of:
a = 155.55 inches and b = 306.52 inches.

The mistake was that 12² was calculated incorrectly. 12² means '12 squared', which is 12 × 12. Of course, 12 × 12 is 144, but the student worked out 12 × 2, which is 24.

Therefore, to work out the correct answer, the student has to replace 24 with 144 and continue to work out the

A = πr²

A = 3.14 · 12²

A = 3.14 · 144

A = 452.16 yd²