By the word "dilation" we mean to say that the dimension of the new triangle is 6 times longer than the dimensions of the former triangle. The ratio between the area of the new triangle and the old one is equal to the square of the ratio of their sides. If we let x be the area of the larger triangle then,
(x / 2/3 cm²) = (6/1)²
The value of x from the equation is 24. Thus, the area of the larger triangle is equal to 24 cm².