A square pyramid is a three-dimensional geometric shape with several distinct attributes. Here are the key attributes of a square pyramid:
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Base:
- The base of a square pyramid is a square, which has four equal sides and four right angles.
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Vertices:
- A square pyramid has a total of five vertices: four vertices at the corners of the square base and one vertex at the apex (the point where all the triangular faces meet).
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Edges:
- There are eight edges in a square pyramid: four edges forming the base and four edges connecting the apex to each vertex of the base.
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Faces:
- A square pyramid has five faces: one square face (the base) and four triangular faces that meet at the apex.
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Height:
- The height of a square pyramid is the perpendicular distance from the apex to the center of the base.
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Slant Height:
- The slant height is the length of the line segment from the apex to the midpoint of a side of the base. It is the height of each triangular face.
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Lateral Surface Area:
- The lateral surface area of a square pyramid can be calculated using the formula: \[ \text{Lateral Surface Area} = \frac{1}{2} \times \text{Perimeter of the base} \times \text{Slant height} \]
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Total Surface Area:
- The total surface area is the sum of the lateral surface area and the area of the base: \[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of the base} \]
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Volume:
- The volume of a square pyramid can be calculated using the formula: \[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
These attributes characterize a square pyramid and are fundamental to understanding its geometric properties.