Lesson · Grade 8 · Mathematics
Volume of a Triangular Prism
- Grade 8
- Mathematics
- 2 min 3 s
- British Columbia
- BC8-MA-28
A tent-shaped triangular prism is named by its cross-section, which is shown sliding 10 cm along to sweep out the solid. The base area is worked out as 6 × 4 ÷ 2 = 12 cm², giving 12 × 10 = 120 cm³, and the answer is checked against the common mistake of forgetting to halve (240 cm³, the whole box). The same rule, cross-section area × length, then gives 90 cm³ for a right prism with a trapezoid cross-section (parallel sides 4 cm and 8 cm, 3 cm high, 5 cm long).
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In one sentence
The question this lesson answers
How much space is inside this tent?
That amount is its volume, measured in cubic centimetres.
Transcript
What the lesson says
How much space is inside this tent?
That amount is its volume, measured in cubic centimetres.
It is a triangular prism: every slice straight across is the same triangle, called the cross-section.
The triangle is 6 centimetres wide and 4 centimetres high, and the prism is 10 centimetres long.
Slide the triangle 10 centimetres along, and it sweeps out the whole prism.
So the volume of a prism like this is its cross-section area times its length.
A triangle's area is base times height divided by 2, since it fills half a rectangle.
6 times 4 is 24, and half of 24 is 12 square centimetres.
Each 1 centimetre slice holds 12 cubic centimetres, so 12 times 10 is 120 cubic centimetres.
A common mistake is forgetting to halve: 6 times 4 times 10 is 240, the whole box.
The tent is half of that box, and half of 240 is 120, so our answer checks out.
The same rule works for any right prism, where the length is at right angles to the ends.
This cross-section is a trapezoid, a quadrilateral with one pair of parallel sides, 4 and 8 centimetres long.
The trapezoid is 3 centimetres high, and the prism is 5 centimetres long.
Average the parallel sides and multiply by the height: 4 plus 8 is 12, half of 12 is 6, and 6 times 3 is 18 square centimetres.
Multiply by the length: 18 times 5 is 90 cubic centimetres.
For any right prism, the volume is the cross-section area times the length.
Curriculum
Where this fits
- British Columbia, Grade 8
Mathematics, Geometry and measurement: surface area and volume of regular solids, including triangular and other right prisms and cylindersBC8-MA-28
Previous: Volume Is the Area of the Base Times the HeightNext: Volume of a Cylinder: Base Area Times Height
The outcomes and strands follow the British Columbia curriculum.
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