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Subsection 2.7.11 Volume of a Triangular Prism

Activity 2.7.15.

Work together in small groups of 5 to:
Discuss ideas
Distribute tasks (e.g., measuring, cutting, assembling)
Share calculations
  • Building a Bridge
    \(\text{V } = \text{Base Area} \times \text{Height}\)
    where the base area is given by \(\frac{1}{2} \times \text{Base} \times \text{height of the triangle}\text{.}\)
Skills to be Developed: Measurement, visualization, real-world connection
  • Materials needed:
    ● Cardboard or wooden sticks
    ● triangular prisms
    ● Using the cardboards or wooden sticks construct a bridge model with the triangular prism acting as supports as shown alongside.
    ● Have them measure the base, height of the triangle, and length of the prism.
  • Use the formula to calculate the volume of the prism-shaped supports.
  • Compare different bridge designs and discuss which structure is the strongest.
    Why Choose the "Build a Bridge" Activity?
    ● Bridges are a perfect example of triangular prisms in engineering. Many bridges use triangular trusses because they:
    Distribute weight evenly
    Provide structural stability
    Are used in real-life construction
    ● By building a model bridge, students get to see, touch and manipulate triangular prisms, helping them connect abstract mathematical concepts to real-world engineering.
    \(\textbf{More Than Just Math!} \)
    The \(\textbf{"Build a Bridge"} \)activity isn’t just about calculating volume—it’s about seeing math in action!

Example 2.7.37.

Find the Surface area of the triangular prism below.
Solution.
Step 1: Find the area of the base.
\begin{align*} \text{area of a triangle} = \amp \frac{1}{2} b\, \times \,h\\ = \amp \frac{1}{2} \times 8 \text{cm} \times 12\, \text{cm} \\ = \amp 48\, \text{cm}^2 \end{align*}
Step 2: Multiply the area of the base by the height of the solid to find the volume
\begin{align*} \text{volume} = \amp \text{area of base} \times \text{height}\\ = \amp \frac{1}{2} b \times h \times H\\ = \amp 48 \,\text{cm}^2 \times 12\, \text{cm} \\ = \amp 576\, \text{cm}^3 \end{align*}
The volume of the triangular prism is\(\, 576 \, \text{cm}^3\)
\(\textbf{Exercise}\)
1. A triangular prism has a volume of 360 cm³. The base of the triangular cross-section is 10 cm, and the height of the triangle is 9 cm. Find the length of the prism.
2. A water trough is in the shape of a triangular prism. The triangular cross-section has a base of 10 cm and a height of 12 cm. The trough is 2 meters long. How much water can it hold in liters? (Hint: 1 cm³ = 1 mL, and 1,000 mL = 1 L)
3. A triangular prism has a triangular base with a base length of 8 cm and a height of 6 cm. Find the total volume of the solid.
4. A storage container is shaped like two triangular prisms joined together along their rectangular faces. Each triangular prism has a base of 5 cm, a height of 4 cm, and a length of 20 cm. Find the total volume of the container.
5. A house-shaped block consists of a rectangular prism 6 cm by 8 cm by 12 cm with a triangular prism (with a base of 8 cm and a height of 6 cm) attached on top. The figures below shows the blocks whey they are divided into two equal halves. Find the total volume of the solid.
6. A company manufactures Toblerone-shaped chocolate bars, which are shaped like triangular prisms. Each bar has a triangular cross-section with a base of 5 cm and a height of 4 cm, and the length of the chocolate bar is 30 cm. Find the volume of a single chocolate bar. If 100 bars are packed into a box, what is the total volume of chocolate in the box?
7. An architect designs a triangular prism-shaped roof for a house. The triangular cross-section has a base of 6 m and a height of 4 m. The length of the roof is 12 m. Calculate the total volume of the roof structure.