CPM Homework Help : GC Problem 9-49

oblique prism with the following labels: top shaded rectangle, left edge is 7 inches, top edge is 13 inches, slanted right side back edge is 12 inches. Elliot has a modern fish tank that is in the shape of an oblique prism, shown at right. If the slant of the prism makes a $60°$ angle, find the volume of water the tank can hold. Assume all measurements are in inches.

Hint (a):

Use a special right triangle to find the height of the parallelogram.

Two similar right triangles. The large triangle has a height of, h, and a hypotenuse of 12. The smaller triangle has a height of the square root of 3, a base of, 1, and a hypotenuse of 2.

Step 1(a):

Find the height of the parallelogram:

$\text{linear scale factor}=6$

$h=6(1\sqrt{3})=6\sqrt{3}$

Step 2 (a):

Find the volume:

$\text{V} = 7 \cdot 13 \cdot 6\sqrt{3} = 546\sqrt{3}$

Answer (a):

$\approx 945.7\: \text{in.}^3$