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Home > PC3 > Chapter 3 > Lesson 3.1.2 > Problem 3-33


3 dimensional Equilateral triangular prism, sitting on one of its edges, with the triangular bases, front & back. Each side of front triangle, is labeled, x, and bottom edge of prism, is labeled, 12 feet. A trough is in the shape of an equilateral triangular prism, as shown in the diagram at right. The length of the trough is feet.  

  1. Write an equation for the height of the equilateral triangle in terms of .

    Draw and label the triangle with information you know. Use the Pythagorean Theorem to solve for the height.

    Equilateral triangle, horizontal side on top, with dashed segment from bottom vertex, perpendicular to the top side, labeled, question mark. Left section of top side, labeled 1 half x,  Left slanted side, labeled, x.

  2. Write an equation for the volume of the trough in terms of .

    (area of the triangle)(length of the trough)

  3. If the trough can hold of water, how deep is the trough?

    Solve .