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**9-4 Surface Areas of Prisms and Cylinders**

Objective – Find the surface area of prisms and cylinders.

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CA Geometry Standard 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

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**Types of Prisms Lateral Edges Lateral Faces Bases Bases**

Triangular Prism Pentagonal Prism h h Right Prism Oblique Prism

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**Formulas You Need to Remember:**

Area of a Triangle → A = bh ÷ 2 Area of Parallelogram → A =bh Area of Trapezoid → A = h(b1 + b2) ÷ 2

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**Key Concept(s): Lateral Area and Surface Area of a Prism**

Base Perimeter h Lateral Area Base Perimeter Height Base Area Surface Area Lateral Area Area of the Base(s)

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**#1 Finding the Surface Area of a Prism**

Find the surface area of the regular hexagonal prism. P = 36 12 m 6 m

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**#2 Finding the Surface Area of a Prism**

Find the surface area of the triangular prism. 12 cm 5 cm 6 cm P = 16 5 cm

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**Key Concept(s): Lateral Area and Surface Area of a Cylinder Base Area**

Radius Lateral Area Radius Height h Surface Area Lateral Area Base Area

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**#3 Finding the Surface Area of a Cylinder**

Find the surface area of a cylinder with height 10 cm and radius 5 cm in terms of pi. 5 cm 10 cm

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**#4 Finding the Surface Area of a Cylinder**

Find the surface area of a cylinder with radius 6 ft and height 9 ft in terms of pi. 9 ft 6 ft

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Example: Find the surface area of a cylinder with radius 3 ft and height 6 ft. S.A. = 2πrh + 2B 7 ft 5 ft

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**Example: Find the surface area of the triangular prism. S.A. = ph + 2B**

10 cm 5 cm 4 cm 7 cm

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Homework Pre-AP Textbook pg.491 #1-14 Evens

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Prisms & Pyramids 1 Prism and Pyramids Formulas Prisms: Lateral Area: L.A. = ph (p = perimeter, h = height) Surface Area: S.A. = ph + 2B (B = area of base)

Prisms & Pyramids 1 Prism and Pyramids Formulas Prisms: Lateral Area: L.A. = ph (p = perimeter, h = height) Surface Area: S.A. = ph + 2B (B = area of base)

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