PrismsLesson 11-2

2 Truths and a fib!

1. A cylinder is not a polyhedron.

3. A square pyramid has 5 faces.

2. A cuboid is a type of pyramid.

What is a prism? A prism is a 3D figure with parallel basesthat are polygons The name of a prism tells what the baseshould be shaped like:

– Triangular prism – triangle bases – Rectangular prism – rectangle bases – Cube – square bases – Pentagonal prism – pentagon bases

These are the facts…

•The bases are NOT always the top and bottom.

•The height is NOT always vertical.

•The faces are ALWAYS rectangles.

•The bases are ALWAYS parallel & congruent.

What’s the difference?

Lateral Area Surface Area

•Only the area of the faces

•NOT including thebases

•The area of ALL the faces

•including the bases

A cube is a prism. Remember that in acube all sides are the same.

Lateral area=?

Side length is 5 inches

Total Surface area=?

Lateral area=4s2=4(5)2=100in2

Total Surface area=6s2=6(5)2=150in2

CUBELateral area and Surface area

Volume of a Cube

Side length is 5 inches

Volume= area of base x heightV = Bh (B= AREA of the base)

Area of the base=5(5) =25Height=5Volume= 125 cubic inches

Area of the base=?Height=?Volume= ?

54

8

Lateral Area of a Rectangular Lateral Area of a Rectangular PrismPrism

There are 2 sides: 5 by 8 = 2(40)=80There are 2 sides: 4 by 8 = 2(32)=64Lateral area = 144 sq. units

To find lateral area: find area of 4 sides, not the parallel bases.

Total Surface Area of a Rectangular PrismSurface Area = Lateral Area + 2 times area of the base

54

8Lateral area = ?Lateral area = ?LA=144 sq. unitsLA=144 sq. units

Now calculate…2 times the area of the base!Now calculate…2 times the area of the base!

Area of the base = 5(4) = 20Area of the base = 5(4) = 2020 times 2 =4020 times 2 =40

SA = 144 + 40 =184 sq. units

Volume of a Rectangular Prism

V = area of base x heightV = Bh (B= AREA of the base)

54

8

Area of base =5 x 4 = 20Area of base =5 x 4 = 20H = 8H = 8

V = 20 x 8 = 160V = 20 x 8 = 160

Area of base =?Area of base =?Height = ?Height = ?

Volume = ?Volume = ?

Triangular PrismLateral Area and Surface Area

Lateral area Lateral area = ?= ?

Surface Area = Lateral Area + 2 times area of the baseArea of the base=?Triangle ½(6)(4) =122 triangles: 24

Lateral area = 3 rectangles!Lateral area = 3 rectangles!

6

8

5

4

4Lateral area =Lateral area =6(4) = 246(4) = 245(4) = 205(4) = 208(4) = 328(4) = 32Total= 76Total= 76

Total SA = 76+24 = 100 sq. unitsTotal SA = 76+24 = 100 sq. units

Triangular PrismVolume

Area of the base=?Triangle ½(6)(4) =12

Volume = BhVolume = Bh

6

8

5

4

4

Height of prism= ?Height of prism= ?

Volume = area of base x heightVolume = area of base x height

Height of prism= 4

Volume= (12)4=48 cubic units