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Questions and Answers
What is the shape of the base of a triangular prism?
What is the importance of the base in a prism?
What is the measurement labeled as 'B' in a prism?
If a prism has a base that is a 4 inch by 4 inch square, what is the area of the base?
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What is the shape of the cross-section if you take a cross-section of a prism anywhere along its length?
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What is the formula to find the surface area of a prism?
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What is the measurement that represents how tall the prism stands?
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What is the formula to find the volume of a prism?
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Why do we multiply the area of the base by two in the surface area formula?
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Why do the answers for surface area and volume have units squared and cubed respectively?
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Study Notes
Prisms
- A prism is a three-dimensional object with parallel straight sides and a top and bottom base of the same polygonal shape.
- The base can be any polygonal shape, and the prism is identified by its base shape (e.g. triangular prism, square prism, pentagonal prism).
Real-Life Examples
- Some skyscrapers are shaped like prisms, with parallel straight sides and a rectangular base.
- If a cross-section is taken along the length of the skyscraper, its shape will always be the same as the base.
Measurements
- The area of the base (B) is an important measurement for calculating surface area and volume.
- The perimeter of the base (P) is another important measurement.
- The height of the prism (h) is the third measurement needed.
Surface Area
- The formula for surface area is: Surface Area = 2 * B + P * h.
- This formula includes the area of the base, the perimeter, and the height.
- The surface area is the total area of the prism's surface.
Calculating Surface Area
- Calculate the area of the base and the perimeter before using the surface area formula.
- Plug in the values to find the surface area.
- The surface area is always measured in squared units.
Volume
- The formula for volume is: Volume = B * h.
- The volume is the amount of space inside the prism.
- Calculate the area of the base and multiply it by the height to find the volume.
- The volume is always measured in cubed units.
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Description
Learn about prisms, three-dimensional objects with parallel straight sides and polygonal bases, and how they are identified by their base shapes.
