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Questions and Answers
Which of the following is NOT a defining characteristic of a prism?
Which of the following is NOT a defining characteristic of a prism?
- Enclosing a three-dimensional space.
- Having all faces as regular polygons. (correct)
- Having two congruent and parallel faces.
- Having lateral faces that are parallelograms.
In a prism, what is a lateral edge?
In a prism, what is a lateral edge?
- A line connecting the vertices of the bases.
- A side of the polygon that forms the base.
- A line where the lateral faces intersect. (correct)
- The perpendicular distance between the bases.
What does 'B' represent in the formula for the volume of a prism, $V = Bh$?
What does 'B' represent in the formula for the volume of a prism, $V = Bh$?
- The perimeter of the base.
- The length of one of the lateral edges.
- The total surface area of the prism.
- The area of the base. (correct)
For a right prism, what can be said about the lateral edges in relation to the base?
For a right prism, what can be said about the lateral edges in relation to the base?
If a prism has a lateral area of 60 square units and the area of each base is 20 square units, what is the total area of the prism?
If a prism has a lateral area of 60 square units and the area of each base is 20 square units, what is the total area of the prism?
Flashcards
Polyhedron
Polyhedron
A three-dimensional shape formed by polygons joined along their sides, enclosing a space.
Prism
Prism
A polyhedron with two congruent and parallel polygonal bases and lateral faces that are parallelograms.
Base of a Prism
Base of a Prism
The congruent and parallel faces of a prism; their shape determines the type of prism (e.g., rectangular prism, triangular prism).
Right Prism
Right Prism
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Lateral Area of Prism
Lateral Area of Prism
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Study Notes
Polyhedrons and Prisms
- A polyhedron is a three-dimensional figure composed of polygonal surfaces joined along their edges, enclosing a volume of space.
- A prism is a special type of polyhedron with specific properties:
- It has two congruent and parallel faces (called bases).
- All other faces are parallelograms.
Parts of a Prism
- Base: Congruent, parallel faces that are polygons.
- Base edge: Sides of the polygonal bases.
- Lateral face: The faces other than the bases.
- Lateral edge: Parallel and congruent lines where lateral faces intersect.
- Altitude (or height): Perpendicular distance between the polygonal bases (or the planes containing the bases).
Right vs. Oblique Prisms
- Right prism: Lateral edges are perpendicular to the bases.
- Oblique prism: Lateral edges are not perpendicular to the bases.
- Regular prism: The bases are regular polygons.
Formulas
- Lateral Area (L): L = Ph (where P = perimeter of the base and h = height)
- Total Area (T): T = L + 2B (where B = area of the base)
- Volume (V): V = Bh (where B = area of the base and h = height)
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