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Worksheet: Finding the Volume of a Triangular Prism

Q1:

Determine the volume of the given triangular prism.

Q2:

Determine the volume of the given triangular prism.

Q3:

Determine the volume of the given triangular prism.

Q4:

Consider the shown rectangle.

Write an expanded expression for its area.

  • A 2 π‘Ž π‘₯ βˆ’ 1 0
  • B 2 π‘Ž π‘₯ βˆ’ 4 π‘₯ βˆ’ 1 0
  • C 2 π‘Ž π‘₯ + 5 π‘Ž βˆ’ 1 0
  • D 2 π‘Ž π‘₯ βˆ’ 4 π‘₯ + 5 π‘Ž βˆ’ 1 0
  • E π‘Ž π‘₯ βˆ’ 4 π‘₯ + 5 π‘Ž βˆ’ 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 π‘Ž π‘₯ + 1 5 2 π‘Ž βˆ’ 5 π‘Ž π‘₯ βˆ’ 2 5 2 π‘Ž βˆ’ 2 π‘₯ βˆ’ 5 2 2
  • B 6 π‘Ž π‘₯ βˆ’ 1 0 π‘Ž π‘₯ βˆ’ 2 5 π‘Ž βˆ’ 4 π‘₯ βˆ’ 1 0 2
  • C 6 π‘Ž π‘₯ + 1 5 π‘Ž βˆ’ 1 0 π‘Ž π‘₯ βˆ’ 2 5 π‘Ž βˆ’ 4 π‘₯ βˆ’ 1 0 2 2
  • D 6 π‘Ž π‘₯ + 1 5 π‘Ž βˆ’ 1 0 π‘Ž π‘₯ βˆ’ 2 5 π‘Ž βˆ’ 1 0 2 2
  • E 6 π‘₯ π‘Ž + 1 5 π‘Ž βˆ’ 1 0 π‘Ž π‘₯ βˆ’ 2 5 π‘Ž βˆ’ 4 π‘₯ βˆ’ 1 0 2 2

Q5:

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.

Q6:

Work out the volume of the triangular prism shown.

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

Q7:

Consider the shown rectangle.

Write an expanded expression for its area.

  • A 2 π‘Ž π‘₯ βˆ’ 1 0
  • B 2 π‘Ž π‘₯ βˆ’ 4 π‘₯ βˆ’ 1 0
  • C 2 π‘Ž π‘₯ + 5 π‘Ž βˆ’ 1 0
  • D 2 π‘Ž π‘₯ βˆ’ 4 π‘₯ + 5 π‘Ž βˆ’ 1 0
  • E π‘Ž π‘₯ βˆ’ 4 π‘₯ + 5 π‘Ž βˆ’ 1 0

The given rectangle is the base of a triangular prism of height 3 π‘Ž + 1 .

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

  • A 3 π‘Ž π‘₯ + 1 5 2 π‘Ž βˆ’ 5 π‘Ž π‘₯ βˆ’ 2 5 2 π‘Ž βˆ’ 2 π‘₯ βˆ’ 5 2 2
  • B 3 π‘Ž π‘₯ + βˆ’ 5 π‘Ž π‘₯ βˆ’ 2 5 2 π‘Ž βˆ’ 2 π‘₯ βˆ’ 5 2
  • C 3 π‘Ž βˆ’ 5 2
  • D 3 π‘Ž π‘₯ + 1 5 2 π‘Ž βˆ’ 5 π‘Ž π‘₯ βˆ’ 2 5 2 π‘Ž βˆ’ 5 2 2
  • E 3 π‘₯ + 1 5 2 π‘Ž βˆ’ 5 π‘Ž π‘₯ βˆ’ 2 5 2 π‘Ž βˆ’ 2 π‘₯ βˆ’ 5 π‘Ž 2

Q8:

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

Q9:

Answer the following questions for the prism shown.

Work out the volume of the prism.

Work out the surface area of the prism.

Q10:

Find, to the nearest tenth, the volume of the solid formed by the given net.

Q11:

Work out the volume of the triangular prism shown.

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

Q12:

Work out the volume of the prism shown.

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

Q13:

A triangular prism of volume 132 yd3 has height 11 yd. If the triangular section has altitude 6 yd, what is this triangle’s base?

Q14:

Work out the volume of the trapezoidal prism shown.