Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Question

Ms. Chang asked the class to find the volume of this oblique regular polygon prism. What answer should the students come to?

### Understanding Prism Dimensions Ms. Chang asked the students to study the dimensions of the given 3D shape. How should the students proceed to understand the properties of this prism? In the image above, we see a three-dimensional drawing of a prism with the following dimensions marked: - **Height of the prism**: 21 units - **Depth of the prism**: 19 units - **Length of the base side**: 7 units - **Height of the triangular base**: 3 units The prism is oriented such that the triangular base is prominently visible at the bottom-left corner of the diagram. Additional visual features include bold lines representing the edges of the prism and dotted lines indicating hidden edges and the measurements of the depth. ### Analysis of the Diagram To comprehend the volume of the prism, the students should consider the following steps: 1. **Calculate the Area of the Triangular Base**: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 3 = 10.5 \text{ square units} \] 2. **Calculate the Volume of the Prism**: \[ \text{Volume} = \text{Base Area} \times \text{Height of the Prism} = 10.5 \times 21 = 220.5 \text{ cubic units} \] Understanding such diagrams is crucial for visualizing geometric properties and efficiently solving related mathematical problems.
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Transcribed Image Text:### Understanding Prism Dimensions Ms. Chang asked the students to study the dimensions of the given 3D shape. How should the students proceed to understand the properties of this prism? In the image above, we see a three-dimensional drawing of a prism with the following dimensions marked: - **Height of the prism**: 21 units - **Depth of the prism**: 19 units - **Length of the base side**: 7 units - **Height of the triangular base**: 3 units The prism is oriented such that the triangular base is prominently visible at the bottom-left corner of the diagram. Additional visual features include bold lines representing the edges of the prism and dotted lines indicating hidden edges and the measurements of the depth. ### Analysis of the Diagram To comprehend the volume of the prism, the students should consider the following steps: 1. **Calculate the Area of the Triangular Base**: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 3 = 10.5 \text{ square units} \] 2. **Calculate the Volume of the Prism**: \[ \text{Volume} = \text{Base Area} \times \text{Height of the Prism} = 10.5 \times 21 = 220.5 \text{ cubic units} \] Understanding such diagrams is crucial for visualizing geometric properties and efficiently solving related mathematical problems.
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