A triangle with an area of 23 cm² is dilated by a factor of 6.

For this item, I will assume that we are required to give the area of the dilated triangle. By dilated we mean to say that the dimensions of the second triangle is 6 times that of the first. We square 6 and them multiply this to the area of the original triangle to get the area of the second. That is,

area of second triangle = (2/3 cm²) (6²) = 24 cm²

Thus, the area of the new triangle is equal to 24 cm².