Atriangle has an area of 30 cm². the base and height are scaled by a factor of 3.

what is the area of the resulting triangle?

The answer is 270 cm²

The area (A) of a triangle with base b and height h is:
A = b * h / 2
A = 30 cm²

Since the base and height are scaled by a factor of 3, that means that they are increased 3 times:
b1 = 3b
h1 = 3h
A1 = b1 * h1 /2
A1 = 3b * 3h / 2
A1 = 3 * 3 * b * h / 2
A1 = 9 * b * h / 2
A1 = 9 * A
A1 = 9 * 30 cm²
A1 = 270 cm²