2012 CEMC Gauss (Grade 7) Problems/Problem 21

Problem

A triangular prism has a volume of $120 cm^{3}$ . Two edges of the triangular prism measure 3 cm and 4 cm, as shown.

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The height of the prism, in cm, is

$\text{(A)}\ 12 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 8$

The volume of the triangular prism will be the area of the base multiplied by its height.

Let $A$ and $h$ be the area of the base and the height, respectively. We then have:

$A = \frac{3 cm * 4 cm}{2} = 6 cm^2$

$A * h = V$

$6 cm^2 * h = 120 cm^3$

$h = \frac{120 cm^3}{6 cm^2} = 20 cm$

Thus, the answer is $\boxed {\textbf {(B) } 20}$ .