002 s.a. of prisms
- 1. OBJECTIVE To find lateral area and surface area of a polyhedron, the prism
- 3. 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.
- 5. A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
- 6. Postulate Write the formula for the volume of a right rectangular prism. V = lwh We will assume prisms are RIGHT from now on
- 7. Vocabulary Polyhedron- A geometric solid with polygons as faces.
- 8. NEW DEFINITION Prism-A polyhedron with two polygonal bases that are parallel and congruent.
- 9. Right Prism - lateral edges are perpendicular to the planes of the bases.
- 10. Vocabulary Altitude of a Prism - any segment perpendicular to the planes containing the bases with endpoints in these planes. ( same as HEIGHT)
- 11. Vocabulary Net - a figure that can be folded to enclose a particular solid figure
- 12. Classwork Draw a net for a right triangular prism. Draw a net for a right pentagonal prism.
- 13. Classwork
- 14. Classwork
- 15. 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.
- 16. 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.
- 17. 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.
- 18. 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.
- 19. 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
- 20. Classwork
- 21. LATERAL AREA
- 22. SURFACE AREA
- 23. 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.
- 24. Lateral Area of a Right Prism Is their a short cut for finding the lateral area ?
- 25. 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
- 26. 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
- 27. Volume Volume equals Area of the Base times the Height of the object. V = BH Area of the Base x Height of the object
- 30. 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.
- 31. 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)
- 32. Example 1: Drawing Orthographic Views of an Object Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 33. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes. Bottom
- 34. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 35. Example 1 Continued Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 36. Check It Out! Example 1 Draw all six orthographic views of the given object. Assume there are no hidden cubes.
- 37. Check It Out! Example 1 Continued
- 38. Classwork/Homework Practice and Apply 7.2 P685 #’s 13-26 and 28-31