Math Problem Statement

Calculate the volume of this triangular prism.

Solution

To calculate the volume of the triangular prism:

Step 1: Formula for the volume of a triangular prism:

Volume=Base Area×Height of the Prism\text{Volume} = \text{Base Area} \times \text{Height of the Prism}

Step 2: Calculate the area of the triangular base:

The base is a right triangle with:

  • One leg = 5 cm
  • Other leg = 8 cm

The formula for the area of a triangle: Base Area=12×Base×Height\text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} Base Area=12×8×5=20cm2\text{Base Area} = \frac{1}{2} \times 8 \times 5 = 20 \, \text{cm}^2

Step 3: Multiply by the height of the prism:

The height of the prism is the length perpendicular to the base, which is given as 11cm11 \, \text{cm}. Thus: Volume=Base Area×Height\text{Volume} = \text{Base Area} \times \text{Height} Volume=20×11=220cm3\text{Volume} = 20 \times 11 = 220 \, \text{cm}^3

Final Answer:

The volume of the triangular prism is 220cm3.\text{The volume of the triangular prism is } 220 \, \text{cm}^3.

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Explore More:

  1. What is the formula for the surface area of a triangular prism?
  2. How does the volume formula change for different prisms?
  3. What are examples of real-life objects shaped like triangular prisms?
  4. Can you derive the area of the triangular base for other types of triangles?
  5. How do you calculate the centroid of a triangular prism?

Tip:

When solving geometry problems, always confirm the shape and verify dimensions from the diagram!

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Math Problem Analysis

Mathematical Concepts

Volume calculation
Geometry
Area of triangles

Formulas

Volume = Base Area × Height of the Prism
Base Area = (1/2) × Base × Height

Theorems

Area of a triangle theorem

Suitable Grade Level

Grades 7-9