http://www.ck12.org Chapter 11. Surface Area and Volume
Vocabulary
Aprismis a 3-dimensional figure with 2 congruent bases, in parallel planes, and in which the other faces are
rectangles.
The non-base faces arelateral faces. The edges between the lateral faces arelateral edges. Aright prismis a
prism where all the lateral faces are perpendicular to the bases. Anoblique prismis a prism that leans to one side
and whose height is perpendicular to the base’s plane.
Surface areais a two-dimensional measurement that is the sum of the area of the faces of a solid. Volumeis a
three-dimensional measurement that is a measure of how much three-dimensional space a solid occupies.
Guided Practice
- Find the surface area of the regular pentagonal prism.
- Find the volume of the right rectangular prism below.
- Find the volume of the regular hexagonal prism below.
- Find the area of the oblique prism below.
Answers:
- For this prism, each lateral face has an area of 160units^2. Then, we need to find the area of the regular pentagonal
bases. Recall that the area of a regular polygon is^12 asn.s=8 andn=5, so we need to finda, the apothem.
tan 36◦=4
a
a=4
tan 36◦≈ 5. 51
SA= 5 ( 160 )+ 2
(
1
2
· 5. 51 · 8 · 5
)
= 1020. 4
- A rectangular prism can be made from any square cubes. To find the volume, we would simply count the cubes.
The bottom layer has 20 cubes, or 4 times 5, and there are 3 layers, or the same as the height. Therefore there are 60
cubes in this prism and the volume would be 60units^3. - Recall that a regular hexagon is divided up into six equilateral triangles. The height of one of those triangles
would be the apothem. If each side is 6, then half of that is 3 and half of an equilateral triangle is a 30-60-90 triangle.
Therefore, the apothem is going to be 3
√
- The area of the base is:
B=
1
2
(
3
√
3
)
( 6 )( 6 ) = 54
√
3 units^2And the volume will be:
V=Bh=(
54
√
3
)
( 15 ) = 810
√
3 units^3- This is an oblique right trapezoidal prism. First, find the area of the trapezoid.
B=
1
2
( 9 )( 8 + 4 ) = 9 ( 6 ) = 54 cm^2