Surface Area and Lateral Surface Area of Prisms:
What is a prism?
What are the bases of a prism?
What are the lateral faces of a prism?
What is the height of a prism?
1. Here are two views of our hexagonal prism.
The bases are hexagons: What is the area of each base?
What is the height of this prism?
The lateral faces are rectangles.
How many lateral faces are there?
What is the area of each lateral face?
What is the total lateral area (area of all of the lateral faces)?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
2. Here are two views of an isosceles trapezoidal prism.
Find the area of each of the isosceles trapezoidal bases.
This prism has four lateral faces, which are not all congruent.
What is the height of this prism?
Find the area of each of the four lateral faces:
,
,
,
What is the total lateral area of this prism?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
Now, let’s see if we can come up with a shortcut for finding the lateral area
of a prism, when the lateral faces are not all congruent:
Lateral Area of a Prism=
USE OUR FORMULAS AND YOUR UNDERSTANDING OF AREA TO ANSWER:
3. Here is a trapezoidal prism. The trapezoid is not isosceles.
4 cm
Find the area of each trapezoidal base:
What is the perimeter of the trapezoid?
12cm
What is the height of the prism?
What is the lateral area of this prism:
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
4. Here is an equilateral triangular prism.
Find the exact area of each base (leave in terms
of radicals):
Since the base is regular, all of the lateral faces
are congruent. What is the area of each lateral face?
What is the total lateral area?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
5 cm
5. Here is a rectangular prism. In the case of a
rectangular prism, we need to decide which
rectangles are the bases. I have labeled the bases
on the rectangular prisms.
What is the area of a base?
What is the perimeter of the base?
What is the height of the prism?
What is the lateral area of the prism?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
6. Here is a second rectangular prism.
What is the area of a base?
What is the perimeter of the base?
What is the height of the prism?
What is the lateral area of the prism?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
7. Here is a square prism. This is a type
of rectangular prism.
What is the area of a base?
What is the perimeter of the base?
What is the height of the prism?
What is the lateral area of the prism?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
8. Our last one is a prism whose base is an
isosceles right triangle.
What is the area of a base?
What is the exact length of the missing side of the
base?
What is the perimeter of the base?
What is the height of the prism?
What is the lateral area of the prism?
What is the total area of the prism:
Add the area of TWO bases and the lateral area.
The
triangle.
NOTE: The triangle is not a right triangle!
a) Use the perimeter of the base times the height of the prism. Look carefully
at the picture to find the perimeter.
b) Careful in finding the area of the base (the triangle). What is the height of
the triangle (different from the height of the prism)?