prisms lesson 11-2 2 truths and a fib! 1. a cylinder is not a polyhedron. 3. a square pyramid has 5...
TRANSCRIPT
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