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Prisms and Pyramids

Mrs. Moy

Lesson 9-2: Prisms & Pyramids 2

Right Prisms

Lateral Surface Area (LSA) of a Prism = Ph Total Surface Area (TSA) = Ph + 2B

or = [Lateral Surface Area + 2 (Area of the base)](P = perimeter of the base, h = height of prism, B = base area)

Volume of a Prism (V )= Bh

h

h

h

Triangular Prism

Lesson 9-2: Prisms & Pyramids 3

Examples: rectangular prism

54

8

Perimeter of base = 5+5+4+4 = 18

B = 5 x 4 = 20

LSA= P x h or 18 x 8 = 144 sq. units

TSA = LSA (Ph) + 2B = 144 + 2(20) = 184 sq. units

V = B h = 20 x 8 = 160 cubic units

h = 8

Example: Triangular Prism

Lesson 9-2: Prisms & Pyramids 4

6

45

3

h = 3 cm

LSA= Ph = [6+5+5] 3 = 16 x 3 = 48 sq. cm

5TSA= Ph + 2B or LSA + 2BTSA = [6+5+5]3 + 2[1/2 bh] or 48 + 2[1/2 (6x4)] = 48 + 2[1/2 (24)] = 48 + 2[ 12] = 48 + 24 = 72 sq. cm

V = Bh, B= Area of Triangle = ½ bh, B = ½ 6 x 4= 12h = 3, V = 12 x 3 = 36 cubic cm.

B =Area of the Triangle = ½ bh

Practice: Find the LSA and the TSA of this rectangular prism.

• LSA: Ph = Perimeter of the Base x height of the prism.

= [3+3+4+4 ] x 10 = [14 x 10] = 140 cm.

TSA: Ph + 2B = 140 + 2 (3 x 4)

TSA = 140 + 2 (12) = 140 + 24 = 164 sq. cm

Lesson 9-2: Prisms & Pyramids 5

3 cm

4 cm10 cm

Lesson 9-2: Prisms & Pyramids 6

Regular Pyramids

A regular pyramid has a base which is always a regular polygon. The lateral faces all intersect at a point called the vertex and form

triangles. The altitude is a segment from the vertex perpendicular to the base. The slant height is the height of a lateral face.

Lateral side

vertex

altitude

Slant height

Base

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Regular Pyramid( P = perimeter of the base, l = slant height, B = base area)

LSA = ½ (40)(13) = 260 sq. units

Perimeter = 10+10+10+10 = 40

Slant height l = 13 ; Height h = 12

Lateral surface area of a regular pyramid (LSA)= ½ PlSurface area of a regular pyramid (TSA)= ½ Pl+ BVolume of a pyramid (V)= ⅓ Bh

Area of Base = 10 x 10 = 100 sq. units

TSA = 260 + 100 = 360 sq. units

Volume = ⅓ (100)(12) = 400 cubic units⅓ (100)(12) = 400 cubic units1010

13

12

Example:

Practice: Pyramid

Find the LSA, TSA and the Volume of this square pyramid. LSA = ½ P l TSA = LSA (1/2 P l ) + B (area of Base) LSA = 64 sq. units TSA = 80 sq. units Volume = 1/3 Bh = 32 cubic units

8

l = 8

b = 4

h = 6

Prism and Pyramids Formulas

Prisms and Cylinders:

• Lateral Surface Area = Ph (P = perimeter, h = height)

• Total Surface Area = Ph + 2B (B = area of base)

• Volume: V = Bh

Regular Pyramids:

• Lateral Surface Area = ½ Pl (P = perimeter, l = slant height)

• Total Surface Area = ½ Pl + B (B = area of base)

• Volume: V = ⅓ Bh ( B = area of base, h = height)