A three-dimensional right rectangular prism, also known as a rectangular box or cuboid, has several key attributes:
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Faces: A right rectangular prism has six faces, all of which are rectangles. Opposite faces are congruent.
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Edges: It has 12 edges. Each edge is a line segment where two faces meet, and the lengths of these edges correspond to the dimensions of the prism.
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Vertices: There are 8 vertices (corners) where the edges meet.
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Dimensions: The prism is defined by three dimensions: length (l), width (w), and height (h). These dimensions correspond to the lengths of the edges.
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Volume: The volume (V) of a right rectangular prism can be calculated using the formula: \[ V = l \times w \times h \] This represents the amount of space inside the prism.
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Surface Area: The surface area (A) of a right rectangular prism can be calculated using the formula: \[ A = 2(l \times w + l \times h + w \times h) \] This gives the total area of all six rectangular faces.
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Right Angles: All angles formed between adjacent edges and faces are right angles (90 degrees).
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Orientation: The prism can be oriented in various ways, but a right rectangular prism specifically has edges that are aligned with the coordinate axes in three-dimensional space.
These attributes make the right rectangular prism a fundamental shape in geometry and a common object in everyday life.