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Panorama 12

From Polygons to Polyhedrons. Panorama 12. SI UNITS Remember: KING HENRY DIED MOTHER DIDN’T CARE MUCH Km hm dam m dm cm mm For basic units X10 per step going from left to right, ÷10 per step going from right to left

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Panorama 12

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  1. From Polygons to Polyhedrons Panorama 12

  2. SI UNITS Remember: KING HENRY DIED MOTHER DIDN’T CARE MUCH Km hm dam m dm cm mm For basic units X10 per step going from left to right, ÷10 per step going from right to left Ex: change into km:10cm,100dam,52mm,17hm Ex: change into mm: 33km, 6dm, 11cm, 86.5dm Unit 12.1: Polygons

  3. SI UNITS OF AREA For area you can still follow: KING HENRY DIED MOTHER DIDN’T CARE MUCH However, the only difference is multiply by X100 going from left to right, and ÷100 from right to left. The reason for this is since the units are squared we assume 10 X 10 = 100 Therefore, every step you will have to multiply or divide by 100

  4. The apothem is the measure from the center of the polygon (shape) to the center of one side. Apothem of a regular polygon Apothem

  5. There are 2 methods for finding the area of a polygon: POLYGON: has 5 sides or more ex: pentagon, hexagon, etc. Area of a Regular Polygon

  6. Method 1: Triangle method Divide the polygon into triangles Find the area of 1 triangle Use: A= AT x NT (AT= area of triangle, NT= number of triangles) Use the apothem as your height and the length of your side as your base

  7. Method 2: Perimeter method Find the perimeter of your polygon Use A= (p= perimeter, a= apothem)

  8. Some situations you may have to break up the shape into more manageable pieces (decomposing). Some situations you may have to subtract areas. It is always the bigger area minus the smaller area. Remember you cannot have a negative area. Decomposable polygons and subtracting areas

  9. Textbook P 175-176 #1-10 Workbook P 56-59 Classwork and Homework

  10. A solid is an amount of space that is surrounded by a closed surface. Unit 12.2: Solids

  11. Face: flat or curved surface bounded by edges Edge: Line of intersection between two faces Vertex: a corner shared by more than two edges

  12. How many edges, faces, and vertices does each solid have?

  13. A polyhedron is like a solid. It only has flat sides no curved surfaces (sphere, cone, cylinder) A net of Polyhedron is when you unfold the surface. In a net every face must share a common edge with another face. Net of a Polyhedron

  14. Draw the net of the following;

  15. A prism is a polyhedron with to congruent parallel faces, called bases. Bases are connected by lateral faces (always rectangles) Prisms Lateral faces Bases

  16. Prisms are identified according to the shape of the base. A right prism is one whose lateral faces are rectangles A regular prism is one that is base is a regular polygon

  17. A pyramid is a polyhedron with a base and whose lateral faces are triangles. All faces meet at a common point called an apex. Pyramid

  18. Textbook P 185-188 Workbook p 60-63 Homework and Classwork

  19. The height of a prism is the distance between the two bases. The height of a pyramid is the distance between the apex and the base. The apothem of a pyramid is the distance from the apex to the center of one side of the base. Unit 12.3: Areas prisms and pyramids

  20. To find the area of the base of a pyramid or prism simply use your formulas given in Panorama 10. Remember that pyramids have 1 base and prisms have 2. Area of the Base 2m 5m

  21. The lateral area is the sum of the areas of all the faces of a polyhedron, excluding the bases There are two ways to find lateral area. Find the area of 1 face, using formulas from panorama 10. Then multiply by the number of faces. Lateral Area: Prism 3cm 2cm

  22. The second method you must use: A= perimeter of base X height 8.2m 1.5m

  23. This is the area of the faces excluding the base. There are two ways to find it as well. Add the area of each of the triangular faces A= perimeter of base X apothem 2 Lateral Area: Pyramid A= 5cm h= 4.5 cm Side= 3cm

  24. Total area is the sum of the lateral area and the area of the base or bases. A= lateral area + area of base or bases A decomposable solid follows the same rules as the total area. However, you must subtract the area of the base or side where the solids are joined. Total area and decomposable solids

  25. Textbook P 195-198 Workbook p 64-67 Homework and Classwork

  26. To solve unknown measurements, ex: when the height, apothem, etc. are not given, you must; Make sure that there is only one piece of information that is missing. Follow notes from unit 10.3 “Solving equations” (algebra) Unit 12.4: Determining unknown measurements

  27. When solving equations your objective is to get an answer for your letter (missing value). Remember your must get all your letters on one side and numbers on the other. Start with addition and subtraction. Bring them to the other side and change the sign. Remember to keep your variable positive. Get rid of multiplication and division, by doing the opposite operations. Solving Equations

  28. 5. Get rid of any numbers that are squared, by taking the square root. REMEMBER YOUR UNITS Textbook p. 202-204 #1-12 Workbook p. 68-71

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