7th Grade - Prisms

Introduction

  • A prism is a three-dimensional solid (polyhedron) with a pair of identical and parallel faces at opposite ends (called bases of the prism).
  • A prism is named after its base.
  • There are different prisms named based on the shape of their bases. Here are some examples:

  • The height h of a prism is the perpendicular distance between the two bases.

Volume of a Triangular Prism

  • A prism's volume with the area of the base B and height h can be calculated using the formula mentioned below.

Volume=B×h

  • For a triangular prism with a base having altitude a, length of the base b, and height h:

  • For a triangular prism with a base having equal sides s:

Surface Area of a Triangular Prism

  • A triangular prism has 2 triangular bases and 3 lateral faces (parallelogram).
  • The lateral area of a triangular prism: LA=p×h, where p=the perimeter of the base
  • The total area of a triangular prism: TA=LA+2B=p×h+2B

Volume of a Rectangular/Square Prism

  • A prism's volume with the area of the base B and height h can be calculated using the formula mentioned below.

Volume=B×h

  • For a rectangular prism (cuboid) with a base having length l, width w, and height h:

  • For a square prism (cuboid) with a base having equal sides s:

 

Surface Area of a Rectangular/Square Prism

  • A rectangular prism has 2 rectangular bases and 4 lateral faces (parallelogram).
  • A square prism has 2 square bases and 4 lateral faces (parallelogram).
  • The lateral area of a rectangular/square prism: LA=p×h, where p=the perimeter of the base
  • The total area of a rectangular/square prism: TA=LA+2B=p×h+2B

Solved Examples

Question 1: Find the volume of the following triangular prism.

Solution: Volumeprism=B×h

=12×b×a×h

=12×5×7×12

=5×7×6

=210 cm3

 

Question 2: Find the total surface area of the rectangular prism shown below.

Solution: TAprism=p×h+2B

=26+4×20+26×4

=20×20+2×10

=400+20

=420 in2

Cheat Sheet

  • For any prism with the area of base B, height h, and perimeter of base p:
    • Volume, Volumeprism=B×h
    • Lateral Surface Area, LAprism=p×h
    • Total Surface Area, TAprism=LAprism+2B=p×h+2B

Blunder Areas

  • In finding the volume or surface area of a triangular prism, students need to differentiate between the triangle's height (altitude) and the prism's height.
  • A prism can have triangle, square, rectangular, pentagonal, and other polygon shapes as the base but not curved ones such as a circle.