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Prisms with Examples
Prisms
Go to Surface Area or Volume .
A prism is a solid object with:
identical ends
flat faces
and the same cross section all along its length !
A cross section is the shape made by cutting straight across an object.
The cross section of this object is a triangle ...
.. it has the same cross section all along its length ...
... so it's a triangular prism.
▶
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Try drawing a shape on a piece of
paper (using straight lines)
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Then imagine it extending up from the sheet of paper ...
... that's a prism !
No Curves!
A prism is a polyhedron , which means all faces are flat!
No curved sides.
For example, a cylinder is not a prism, because it has curved sides.
Bases
Bases
The ends of a prism are parallel
and each one is called a base.
Parallel
Sides
Parall
el
The side faces of a prism are parallelograms
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(4-sided shapes with opposite sides parallel)
These are all Prisms:
Square Prism:
Cross-Section:
Cube:
Cross-Section:
(yes, a cube is a prism, because it is a square
all along its length)
(Also see Rectangular Prisms )
Triangular Prism:
Cross-Section:
Pentagonal Prism:
Cross-Section:
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Prisms with Examples
and more!
Example: This hexagonal ice crystal.
It looks like a hexagon, but because it has some thickness it is
actually a hexagonal prism!
Photograph by NASA / Alexey Kljatov.
Regular vs Irregular Prisms
All the previous examples are Regular Prisms, because the cross section is regular (in other
words it is a shape with equal edge lengths, and equal angles.)
Here is an example of an Irregular Prism:
Irregular Pentagonal Prism:
Cross-Section
It is "irregular" because the
cross-section is not "regular" in shape.
Right vs Oblique Prism
When the two ends are perfectly aligned it is a Right Prism otherwise it is an Oblique Prism:
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Prisms with Examples
Right
Oblique
Surface Area of a Prism
Surface Area =
Length
2 × Base Area
+ Base Perimeter × Length
Area
of Base
Perimeter
of Base
Example: What is the surface area of a prism where the base area is
25 m2, the base perimeter is 24 m, and the length is 12 m:
Surface Area = 2 × Base Area + Base Perimeter × Length
= 2 × 25 m2 + 24 m × 12 m
= 50 m2 + 288 m2
= 338 m2
(Note: we have an Area Calculation Tool )
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Volume of a Prism
The Volume of a prism is the area of one end times the length of the prism.
Volume = Base Area × Length
Example: What is the volume of a prism where the
Length
Area
of Base
base area is 25 m2 and which is 12 m long:
Volume = Area × Length
Perimeter
of Base
= 25 m2 × 12 m
= 300 m3
Play with it here. The formula also works when it "leans over" (oblique) but remember that the
height is at right angles to the base:
Oblique Prism
Volume = 8 × 7.2 × 15 ≈ 864
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And this is why:
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The stack can lean over, but still has the same volume
More About The Side Faces
The side faces of a prism are
parallelograms (4-sided shape with
opposites sides parallel)
A prism can lean to one side, making it an
oblique prism, but the two ends are still
parallel, and the side faces are still
parallelograms!
But if the two ends are not parallel it is
not a prism.
Question 1 Question 2 Question 3 Question 4 Question 5 Question 6
Question 7 Question 8 Question 9 Question 10
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