1. Sec. 11 – 2 Surface Area of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder.

2. I. Surface Area of a Prism  Prism – Is a polyhedron w/ exactly 2 , // faces, called bases.  Name it by the shape of its bases. Bases are Rectangles: Lateral Faces – All faces that are not bases. (Sides)

3. Right Prisms vs Oblique Prisms Right Prism – Edges are Altitudes. Oblique Prism

4. Lateral Area – The sum of the areas of the lateral faces (sides) Right Prisms - Lateral Faces are Rectangles A = lw Base Area – The sum of the areas of the 2 bases Rectangle: A = lw Triangle: A = ½bh Polygon: A = ½bh Total Surface Area = Lateral Area + Base Area

5. Ex.1: Use the net to find the Surface Area of the rectangular Prism. 5cm 3cm 4cm 343 4 3 5 3 Area of Bases: A = lw 12 2 different Lats: A = lw 15201520 SA = LA + BA = 70cm 2 + 24cm 2 = 94cm 2

6. Ex.2: Find the total surface area of the following triangular prism. 6cm 5cm 12cm LA = lw (5 x 12) = 60cm 2 (6 x 12) = 72cm 2 BA = ½bh = ½(6)(4) = 12cm 2 x 2 x 2 24cm 2 5 3 h a 2 + b 2 = c 2 h 2 + 3 2 = 5 2 h = 4 6 192cm 2 SA = LA + BA = 192cm 2 + 24cm 2 = 216cm 2

7. Ex.2: Find the total surface area of the following regular hexagonal prism. LA = lw (10 x 12) = 120m 2 x 6 BA = ½ap = ½(8.7)(60) = 260m 2 x 2 520m 2 720m 2 SA = LA + BA = 720m 2 + 520m 2 = 1240m 2 10m 12m 10 5 30° a Tan 30 = 5/a.577 = 5/a a = 8.7

8. II. Finding Surface Area of a Cylinder  Cylinder  Has 2 , // bases  Base → Circle  C = 2πr  A = πr 2 height r r h r

9. Net of a Cylinder: LA is just a Rectangle! LA = 2  rh r BA =  r 2 Area of a circle Circumference of the circle SA = LA + 2BA

10. Ex.4: SA of a right cylinder 6ft 9ft LA = 2  rh = 2  (6)(9) = 108  ft 2 = 339.3ft 2 Area of Base BA =  r 2 =  (6) 2 = 36  ft 2 x 2 = 72  ft 2 = 226.2 ft 2 SA = LA + BA = 339.3ft 2 + 226.2ft 2 = 565.5ft 2

11. EXAMPLE: Round to the nearest TENTH. Top or bottom circle A = πr² A = π(3.1)² A = π(9.61) A = 30.2 Rectangle C = length C = π d C = π(6.2) C = 19.5 Now the area A = lw A = 19.5(12) A = 234 Now add: 30.2 + 30.2 + 234 = SA = 294.4 in²

12. Practice:  Worksheet

13. What did I learn today??