12'7 Prisms

1
12.7 Prisms
2
A prism is a solid whose sides (lateral sides)
are parallelograms and whose bases are a pair of
identical parallel polygons. A polygon is a
simple closed figure whose sides are line
segments.
Bases
Triangular prism
Rectangular prism
Pentagonal prism
3
The lateral surface area is the sum of the areas
of the lateral faces of the prism
4
Find the lateral surface area of a rectangular
prism that has length of 7cm, with of 6 cm and
height of 4 cm.
4 cm
6 cm
7 cm
Front and back 4 x 7 each 2(28) 56 sq. cm.
2 ends 4 x 6 each 2(24) 48 sq. cm.
Lateral surface area 104 sq. cm.
5
The total surface area is found by finding the
sum of the lateral area faces and the areas of
the bases.
4 cm
6 cm
7 cm
Total S.A. 104 84 188 sq. cm.
Lateral surface area 104 sq. cm.
The top and bottom are the bases. Top area 6 x
7 42 sq. cm. Same for the bottom 42 sq.
cm Area of the bases 2(42) 84 sq. cm.
6
The lateral surface area is the sum of the areas
of the lateral faces of the prism.
B
C
13 in
B
5 in
5 in
11 in
A
B
A
A143
E
C
F
11 in
E
A
C
11 in
12 in
E
D
D
A 55
11 in
12 in
A132
F
D
S.A. 55 143 132 330 sq.in.
F
7
The total surface area is found by finding the
sum of the lateral area faces and the areas of
the bases.
B
B
A1/2(5)(12) 30 sq.in
5 in
5 in
A
C
A
12 in
E
C
E
A1/2(5)(12) 30 sq.in
11 in
5 in
F
12 in
D
D
12 in
Lat. Area 330 Bases area 60 Total S.
A. 390 sq.in
F
8
The volume of a solid is the number of cubes it
takes to fill the solid.The volume of a prism is
found by multiplying the area of the base (B) by
the height of the prism. The height is the
distance between the 2 bases.
9
Find the volume of a rectangular prism that has
length of 7cm, with of 6 cm and height of 4 cm.
4 cm
6 cm
7 cm
10
1 cm
6 cm
7 cm
11
4 cm
6 cm
42 cm³
7 cm
12
Find the volume of the triangular prism.
B
5 in
A
C
E
11 in
D
12 in
F
13
Steel weighs 0.28 . What is the weight
of a rectangular piece of steel 0.25 in. by 15.0
in. by 32.0 in?
14
A swimming pool with a uniform depth of 4 ft
requires a skimmer for every 12,000 gal of water.
The pool is 50 ft long and 32 ft wide. Water
weighs 62.4 and 8.34 lb/gal. how many
skimmers are needed?