Worksheet: Volume of a Triangular Prism

In this worksheet, we will practice finding the volume of a triangular prism to solve real-life problems with triangular prism-shaped solids.

Q1:

Determine, to the nearest hundredth, the volume of the given solid.

Q2:

Determine the volume of the given triangular prism.

Q3:

The shape in the figure is to be submerged in water. How much water, in cubic centimeters, would be displaced by the prism?

Q4:

The solid shown is formed from two congruent triangular prisms placed together with a rectangular prism cut out along its length. Work out the volume of the solid.

Q5:

Consider the shown rectangle.

Write an expanded expression for its area.

  • A 2 𝑎 𝑥 1 0
  • B 2 𝑎 𝑥 4 𝑥 1 0
  • C 2 𝑎 𝑥 + 5 𝑎 1 0
  • D 2 𝑎 𝑥 4 𝑥 + 5 𝑎 1 0
  • E 𝑎 𝑥 4 𝑥 + 5 𝑎 1 0

The rectangle above is the shaded face of the shown triangular prism.

Write an expanded expression for the volume of the prism. Simplify the expression, if possible.

  • A 3 𝑎 𝑥 + 1 5 2 𝑎 5 𝑎 𝑥 2 5 2 𝑎 2 𝑥 5 2 2
  • B 6 𝑎 𝑥 1 0 𝑎 𝑥 2 5 𝑎 4 𝑥 1 0 2
  • C 6 𝑎 𝑥 + 1 5 𝑎 1 0 𝑎 𝑥 2 5 𝑎 4 𝑥 1 0 2 2
  • D 6 𝑎 𝑥 + 1 5 𝑎 1 0 𝑎 𝑥 2 5 𝑎 1 0 2 2
  • E 6 𝑥 𝑎 + 1 5 𝑎 1 0 𝑎 𝑥 2 5 𝑎 4 𝑥 1 0 2 2

Q6:

Consider the shown rectangle.

Write an expanded expression for its area.

  • A 2 𝑎 𝑥 1 0
  • B 2 𝑎 𝑥 4 𝑥 1 0
  • C 2 𝑎 𝑥 + 5 𝑎 1 0
  • D 2 𝑎 𝑥 4 𝑥 + 5 𝑎 1 0
  • E 2 𝑎 𝑥 + 4 𝑥 + 5 𝑎 1 0

The given rectangle is the base of a triangular prism of height 3 𝑎 + 1 .

Write an expanded expression for the volume of the prism. Simplify the expression, if possible.

  • A 3 𝑎 𝑥 + 1 5 2 𝑎 5 𝑎 𝑥 2 5 2 𝑎 2 𝑥 5
  • B 3 𝑎 𝑥 5 𝑎 𝑥 2 5 2 𝑎 2 𝑥 5
  • C 3 𝑎 5
  • D 3 𝑎 𝑥 + 1 5 2 𝑎 5 𝑎 𝑥 2 5 2 𝑎 5
  • E 3 𝑎 𝑥 + 1 5 2 𝑎 5 𝑎 𝑥 2 5 2 𝑎 2 𝑥 5

Q7:

Work out the volume of the triangular prism shown.

  • A60 units2
  • B54 units2
  • C108 units2
  • D27 units2
  • E18 units2

Q8:

Answer the following questions for the prism shown.

Work out the volume of the prism.

Work out the surface area of the prism.

Q9:

Work out the volume of the triangular prism shown.

  • A140 units3
  • B420 units3
  • C130 units3
  • D210 units3
  • E840 units3

Q10:

Work out the volume of the prism shown.

  • A96 unit 3
  • B180 unit 3
  • C60 unit 3
  • D48 unit 3
  • E120 unit 3

Q11:

Work out the volume of the trapezoidal prism shown.