Chapter 10 day 1 s.a. of prisms
- 1. Drill GT Geom 5/7/14 Find the unknown lengths. 1. the diagonal of a square with side length 5 cm 2. the base of a rectangle with diagonal 15 m and height 13 m 3. the height of a trapezoid with area 18 ft2 and bases 3 ft and 9 ft
- 4. OBJECTIVE To find lateral area and surface area of a polyhedron, the prism
- 6. Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces.
- 8. A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
- 9. Postulate Write the formula for the volume of a right rectangular prism. V = lwh We will assume prisms are RIGHT from now on
- 10. Vocabulary Polyhedron- A geometric solid with polygons as faces.
- 11. DEFINITION Prism-A polyhedron with two polygonal bases that are parallel and congruent.
- 12. Right Prism - lateral edges are perpendicular to the planes of the bases.
- 13. Vocabulary Altitude of a Prism - any segment perpendicular to the planes containing the bases with endpoints in these planes. ( same as HEIGHT)
- 14. Vocabulary Net - a figure that can be folded to enclose a particular solid figure
- 15. Classwork Draw a net for a right triangular prism. Draw a net for a right pentagonal prism.
- 16. Classwork
- 17. Classwork
- 18. Example 2A: Identifying a Three- Dimensional Figure From a Net Describe the three-dimensional figure that can be made from the given net. The net has six congruent square faces. So the net forms a cube.
- 19. Example 2B: Identifying a Three- Dimensional Figure From a Net Describe the three-dimensional figure that can be made from the given net. The net has one circular face and one semicircular face. These are the base and sloping face of a cone. So the net forms a cone.
- 20. Check It Out! Example 2a Describe the three-dimensional figure that can be made from the given net. The net has four congruent triangular faces. So the net forms a triangular pyramid.
- 21. Check It Out! Example 2b Describe the three-dimensional figure that can be made from the given net. The net has two circular faces and one rectangular face. These are the bases and curved surface of a cylinder. So the net forms a cylinder.
- 22. Lateral Area of a Prism - sum of the areas of the lateral faces. Surface Area of a Prism - sum of the lateral area and the areas of the two bases
- 23. Classwork
- 24. LATERAL AREA
- 25. SURFACE AREA
- 26. Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face.
- 27. Lateral Area of a Right Prism Is their a short cut for finding the lateral area ?
- 28. Lateral Area of a Right Prism The lateral area LA of a right prism with height h and perimeter of base p is: LA = Hp or L = Hp
- 29. Surface Area of a Right Prism The surface area SA of a right prism with lateral LA and the area of a base B is: SA = LA + 2B or S =L + 2B
- 30. Volume Volume equals Area of the Base times the Height of the object. V = BH Area of the Base x Height of the object
- 33. Lateral Area of a Right Prism Find the lateral area LA of a right prism with height 10cm, if the base is a regular hexagon with side 3cm.
- 34. Find the surface area SA of a right prism with height 10cm, if the base is a regular hexagon with side 3cm.(round answer to nearest hundredth)
- 35. Example 1: Drawing Orthographic Views of an Object Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 36. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes. Bottom
- 37. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 38. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 39. Check It Out! Example 1 Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 40. Check It Out! Example 1 Continued
- 41. Classwork/Homework Practice and Apply 7.2 P685 #’s 13-26 and 28-31
- 42. Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces.
- 44. A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
- 45. Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face.