Area and Volume of Prism

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Introduction

समतलीय सतहहरूले बनेको ठोस वस्तु प्रिज्म हो । यसमा दुई प्रकारका सतह हुन्छन् । माथिल्लो र तल्लो समानान्तर र अनुरूप सतहहरूलाई प्रिज्मको आधार भनिन्छ । आधारबाहेकका सतहहरूलाई छड्के सतह भनिन्छ । प्रिज्मको नाम यसको आधारको आकारअनुसार हुन्छ, जस्तैः प्रिज्मको आधार त्रिभुज भएमा त्रिभुजाकार प्रिज्म, प्रिज्मको आधार आयत भएमा आयातकार प्रिज्म ।

A prism is a polyhedron, with two parallel identical bases facing each other. The other faces of prism are always parallelograms.
Teacher can discuss that, a prism can only have polygon shapes but not the circular shape. Therefore, a prism has:
  1. identical ends (bases)
  2. flat faces (parallelograms)
  3. the same cross section (bases) all along its length
  4. An altitude of a prism is a perpendicular segment that joins the planes of the bases. The height \(h\) of a prism is the length of an altitude.
In this definition
  1. Vertex (plural: vertices): A corner point where two or more edges meet.
  2. Edge: A line segment where two faces meet.
  3. Face: A flat surface of a solid (3D) shape.
Solid Vertices (V) Edges (E) Faces (F) V-E+F=
Triangular Prism 6 9 5 2
Square Base Prism 8 12 6 2
Cube 8 12 6 2
Cuboid 8 12 6 2
Triangular Pyramid 4 6 4 2
Square Base Pyramid 5 8 5 2
Tetrahedron 4 6 4 2

Triangular Prism

A triangular prism is a three-dimensional solid shape that has:
  1. Two identical triangular bases
  2. Three rectangular lateral faces connecting the corresponding sides of the triangles
  3. 5 faces in total (2 triangles + 3 rectangles)
  4. 6 vertices (corner points)
  5. 9 edges (line segments where faces meet)
It is called a prism because it has the same cross-section along its entire length—any slice parallel to the triangular bases will also be a triangle congruent to the base.

Enter the correct number of Vertices (V), Edges (E), and Faces (F) for a triangular prism.

Then check if Euler's formula holds: V − E + F = 2










माथी चित्रमा त्रिभुजाकार आधार भएका प्रिज्म दिइएको छ । उक्त चित्रको अवलोकन गरी सोधिएका प्रश्नको उत्तर दिनुहोस्ः

  1. त्रिभुजाकार आधार भएका प्रिज्मका सबै सतहको नाम लेख्नुहोस् ।
  2. त्रिभुजाकार आधार भएका प्रिज्ममा कुन कुन सतह अनुरूप छन् ?
  3. त्रिभुजाकार आधार भएका प्रिज्ममा किनारा, सतह र शीर्षबिन्दुको सम्बन्ध लेख्नुहोस् ।

Rectangular Prism

A rectangular prism is a three-dimensional solid shape that has:
  1. Two identical rectangular bases
  2. Four rectangular lateral faces connecting the corresponding sides of the bases
  3. 6 faces in total (all rectangles)
  4. 8 vertices (corner points)
  5. 12 edges (line segments where faces meet)
It is called a prism because it has the same cross-section along its entire length—any slice parallel to the rectangular bases will also be a rectangle congruent to the base.

Enter the correct number of Vertices (V), Edges (E), and Faces (F) for a rectangular prism.

Then check if Euler's formula holds: V − E + F = 2










माथी चित्रमा आयताकार आधार भएका प्रिज्म दिइएको छ । उक्त चित्रको अवलोकन गरी सोधिएका प्रश्नको उत्तर दिनुहोस्:

  1. आयताकार आधार भएका प्रिज्मका सबै सतहको नाम लेख्नुहोस् ।
  2. आयताकार आधार भएका प्रिज्ममा कुन कुन सतह अनुरूप छन् ?
  3. आयताकार आधार भएका प्रिज्ममा किनारा, सतह र शीर्षबिन्दुको सम्बन्ध लेख्नुहोस् ।

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