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Prisms Lesson 11-2

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**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.

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**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

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**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.

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**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

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**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

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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

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**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

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**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 = =184 sq. units

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**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

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**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 = = 100 sq. units

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**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

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