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Find Volume of Triangular Prism with Base 6 ft, Height 5.5 ft, Length 11 ft
Mathematics
Middle School (Grade 7-8)
Question Content
Find the volume of the 3D figure with a triangular base (base = 6 ft, height of triangle = 5.5 ft) and length of the prism = 11 ft (or relevant dimension from the diagram).
Correct Answer
181.5 cubic feet (or \( \frac{363}{2} \) ft³)
Detailed Solution Steps
1
1. Identify the shape: A triangular prism (volume = area of triangular base × length of the prism).
2
2. Calculate the area of the triangular base: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Here, base = 6 ft, height = 5.5 ft. So, \( \text{Area} = \frac{1}{2} \times 6 \times 5.5 = 16.5 \, \text{ft}^2 \).
3
3. Determine the length of the prism (distance along the direction perpendicular to the triangular base): From the diagram, this length is 11 ft.
4
4. Calculate the volume: Multiply the area of the base by the length of the prism. \( \text{Volume} = 16.5 \times 11 = 181.5 \, \text{ft}^3 \).
Knowledge Points Involved
1
Volume of a Triangular Prism
The volume of a triangular prism is calculated as the area of the triangular base (using \( \frac{1}{2} \times \text{base} \times \text{height} \)) multiplied by the length of the prism (the distance between the two triangular faces).
2
Area of a Triangle
The area of a triangle is given by \( \frac{1}{2} \times \text{base} \times \text{height} \), where the base is the length of one side, and the height is the perpendicular distance from that side to the opposite vertex.
3
3D Geometric Shapes (Prisms)
A prism has two congruent polygonal bases connected by rectangular (or parallelogram) faces. The volume of any prism is the area of its base multiplied by its length (the distance between the bases).
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