Prisms Lesson 11-2

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.

What is a prism? A prism is a 3D figure with parallel bases that are polygons The name of a prism tells what the base should 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 ALWAYS parallel & congruent. The bases are NOT always the top and bottom. The height is NOT always vertical. The faces are ALWAYS rectangles.

What’s the difference? Surface Area Lateral Area The area of ALL the faces Only the area of the faces including the bases NOT including the bases

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 inches Lateral area=? Lateral area=4s2=4(5)2=100in2 Total Surface area=? Total Surface area=6s2=6(5)2=150in2

Volume of a Cube Volume= area of base x height V = Bh (B= AREA of the base) Side length is 5 inches Area of the base=? Height=? Volume= ? Area of the base=5(5) =25 Height=5 Volume= 125 cubic inches

Lateral Area of a Rectangular Prism 5 4 8 To find lateral area: find area of 4 sides, not the parallel bases. There are 2 sides: 5 by 8 = 2(40)=80 There are 2 sides: 4 by 8 = 2(32)=64 Lateral area = 144 sq. units

Total Surface Area of a Rectangular Prism Surface Area = Lateral Area + 2 times area of the base 5 4 8 Lateral area = ? LA=144 sq. units Now calculate…2 times the area of the base! Area of the base = 5(4) = 20 20 times 2 =40 SA = 144 + 40 =184 sq. units

Volume of a Rectangular Prism V = area of base x height V = Bh (B= AREA of the base) 5 4 8 Area of base =? Height = ? Volume = ? Area of base =5 x 4 = 20 H = 8 V = 20 x 8 = 160

Triangular Prism Lateral Area and Surface Area 6 8 5 4 Lateral area = ? Lateral area = 3 rectangles! Lateral area = 6(4) = 24 5(4) = 20 8(4) = 32 Total= 76 Surface Area = Lateral Area + 2 times area of the base Area of the base=? Triangle ½(6)(4) =12 2 triangles: 24 Total SA = 76+24 = 100 sq. units

Triangular Prism Volume 6 8 5 4 Volume = Bh Volume = area of base x height Area of the base=? Triangle ½(6)(4) =12 Height of prism= ? Height of prism= 4 Volume= (12)4=48 cubic units