The prism below has a height of h units, a length of 2h units, and a width of h units. Assume that the prism is sitting on one of its bases Which of the following could be used as a formula for the later surface area?

A. LSA = (6h)h square units
B. LSA = (3h)h square units
C. LSA = 2h(6h) square units
D. LSA = 2h(h)(h) square units

9514 1404 393

Explanation:

The length of a line segment is computed from the differences between corresponding end-point coordinates. That is, one needs to know the difference of x-coordinates and the difference of y-coordinates. If the point X is on line segment AB and divides it accordingly, then we have the relation ...

  (X - A) : (B - X) = 1 : 2

This will be true for both the x-coordinates and the y-coordinates of the respective differences. Here, that relation evaluates to ...

  (X -A) = (6, 6) -(2, 2) = (4, 4)

  (B -X) = (14, 14) -(6, 6) = (8, 8)

Then the ratios of coordinates are ...

  x-coordinates: 4 : 8 = 1 : 2

  y-coordinates: 4 : 8 = 1 : 2

These are the same ratios, so we can conclude that X is on segment AB and divides it in the required ratio.