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1 Prisms and Pyramids Mrs. Moy

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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

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Lesson 9-2: Prisms & Pyramids 3 Examples : rectangular prism 5 4 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

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Example: Triangular Prism Lesson 9-2: Prisms & Pyramids 4 6 4 5 3 h = 3 cm LSA= Ph = [6+5+5] 3 = 16 x 3 = 48 sq. cm 5 TSA= Ph + 2B or LSA + 2B TSA = [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= 12 h = 3, V = 12 x 3 = 36 cubic cm. B =Area of the Triangle = ½ bh

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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 cm 10 cm

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Lesson 9-2: Prisms & Pyramids6 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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7 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 Pl Surface area of a regular pyramid (TSA)= ½ Pl+ B Volume of a pyramid (V)= ⅓ Bh Area of Base = 10 x 10 = 100 sq. units TSA = 260 + 100 = 360 sq. units Volume = ⅓ ⅓⅓ ⅓ (100)(12) = 400 cubic units 10 13 12 Example:

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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

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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)

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