2. Chapter 12 12.2 Surface Area of Prisms and Cylinders Find the surface area of a prism Find the surface area of a cylinder

3. Definition Prism Prism A polyhedron with two congruent faces, called Bases, that lie in parallel planes. The other faces are called lateral faces Rectangular Prism Triangular Prism Hexagonal Prism

4. How many different prism are there?  Two types of prisms exist, right prisms and oblique prisms Right Prism Oblique Prism

5. Use the diagram to answer the questions 1. Give the mathematical name of the solid. Right Hexagonal based prism 2. What kind of figure is each base? Hexagon 3. What kind of figure is each lateral face? Rectangle 4. How many lateral faces does the solid have? 6 5. Name three lateral edges. EK, DJ, CI, BH, AG, FL

6. Right Prisms  Right prisms are prisms in which the lateral surfaces are perpendicular to the bases  All the lateral surfaces on the prism are rectangles, they CANNOT be anything else!

7. Anatomy of a Right Prism  Lateral surfaces  Intersect the bases  Rectangular  Bases  All equal  Parallel

8. Oblique Prisms  Oblique prisms are prisms where the bases are still parallel, but they are not right on top of each other  The lateral surfaces on these prisms are any parallelogram other than a rectangle!

9. Nets The two dimensional representation of all the faces of a polyhedron is called a net. Cube or Rectangular solid Cylinder

10. Name the solid that can be folded from each net Cylinder Cube Triangular Prism

11. Surface Area  Surface Area – The area of all the combined polygons on a solid  Base – The polygon at the bottom and top of a prism  Lateral Surfaces – The surfaces on a prism that intersect the bases

12. Surface Area of a Right Prism Theorem 12.2 The surface area of a right Prism can be found using the formula S = 2B + Ph. Where B is the area of the base and P is the perimeter of the base and h is the height

13. Find the surface area of each prism Area of Base = 12(5) = 60 Perimeter of Base = 2(12) +2(5) = 34 S = 2(60) + 34(8) = 392 cm 2 Area of Base = 0.5(12)(5) Perimeter of Base = 5 + 12 +13 = 30 S = 2(30) + 30(4) = 180 in 2

14. Find the surface area of the prism The bases are the front and back which are trapezoids Surface Area = 2(54) + 4(18 + 6  5 ) Perimeter of Base = 12 + (3  5) + 6 + (3  5) h = 4 cm Area of 1 base = 6/2(12 + 6) = 54 cm 2 = 18 + 6  5 cm = 233.67cm 2

15. Cylinders Definition: A solid with congruent circular bases that lie in parallel planes Right Cylinder A cylinder where the segment joining the centers of the bases is perpendicular to the bases Lateral area of a cylinder: The area of the curved surface Surface area of a cylinder is the sum of of the lateral area and the area of the bases Theorem 12.3 Surface area of a right cylinder: The surface area of a right cylinder is: S = 2B + Ch Where B is the area of a base and C is the circumference of one base and h is the height.

16. Find the surface Area of the cylinders S = 2(  )(5 2 ) + 2(  )(5)(4) = 90  ft 2 S = 2(  )(4.5 2 ) + 2(  )(4.5)(8.2) = 114.3  cm 2

17. Find the Surface area of the right cylinder S = 2(  )(9 2 ) + 2(  )(9)(17) = S = 468  in 2

18. Given the surface area of the figure, solve for the given variable 208 = 2(4x) + 8(2x + 2(4)) x = 6 97.5 = 2(.5(6)(6)) + (12 +  72)x x = 3

19. Homework # 60 Pg 732-734 18-42 Even 44-47, 50-60