Ms. Chang asked the class to find the volume of this oblique regular polygon prism. What answer should the students come to? ### Understanding Prism DimensionsMs. 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 unitsThe 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 DiagramTo 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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Answered: Ms. Chang asked the class to find the…

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

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter10: Measurement, Area, And Volume

Section10.5: Surface Areas Of Prisms And Cylinders

Problem 1E

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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.

Definition Definition Two-dimentional plane figure composed of a finite number of straight line segments connected to form a closed chain or circuit. A polygonal circuit's segments are known as its edges or sides, and the points where two edges meet are known as its vertices or corners.

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