2 2 Truths and a fib! A cylinder is not a polyhedron. 2. A cuboid is a type of pyramid.3. A square pyramid has 5 faces.
3 What is a prism? A prism is a 3D figure with parallel bases that are polygonsThe 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
5 These are the facts… The bases are ALWAYS parallel & congruent. The bases are NOT always the top and bottom.The height is NOT always vertical.The faces are ALWAYS rectangles.
6 What’s the difference? Surface Area Lateral Area The area of ALL the facesOnly the area of the facesincluding the basesNOT including thebases
7 CUBE Lateral area and Surface area A cube is a prism. Remember that in a cube all sides are the same.Side length is 5 inchesLateral area=?Lateral area=4s2=4(5)2=100in2Total Surface area=?Total Surface area=6s2=6(5)2=150in2
8 Volume of a CubeVolume= area of base x height V = Bh (B= AREA of the base)Side length is 5 inchesArea of the base=?Height=?Volume= ?Area of the base=5(5) =25Height=5Volume= 125 cubic inches
9 Lateral Area of a Rectangular Prism 548To find lateral area: find area of 4 sides, not the parallel bases.There are 2 sides: 5 by 8 = 2(40)=80There are 2 sides: 4 by 8 = 2(32)=64Lateral area = 144 sq. units
10 Total Surface Area of a Rectangular Prism Surface Area = Lateral Area + 2 times area of the base 548Lateral area = ?LA=144 sq. unitsNow calculate…2 times the area of the base!Area of the base = 5(4) = 2020 times 2 =40SA = =184 sq. units
11 Volume of a Rectangular Prism V = area of base x height V = Bh (B= AREA of the base)548Area of base =?Height = ?Volume = ?Area of base =5 x 4 = 20H = 8V = 20 x 8 = 160
12 Triangular Prism Lateral Area and Surface Area 6854Lateral area = ?Lateral area = 3 rectangles!Lateral area =6(4) = 245(4) = 208(4) = 32Total= 76Surface Area = Lateral Area + 2 times area of the baseArea of the base=?Triangle ½(6)(4) =122 triangles: 24Total SA = = 100 sq. units
13 Triangular Prism Volume 6854Volume = BhVolume = area of base x heightArea of the base=?Triangle ½(6)(4) =12Height of prism= ?Height of prism= 4Volume= (12)4=48 cubic units