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Area and Perimeter Triangles, Parallelograms, Rhombus, and Trapezoids

Area and Perimeter Triangles, Parallelograms, Rhombus, and Trapezoids. Mr. Miller Geometry Chapter 10 Sections 1 and 2. Area. Area is the amount of surface space that a flat object has. Area is reported in the amount of square units.

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Area and Perimeter Triangles, Parallelograms, Rhombus, and Trapezoids

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  1. Area and Perimeter Triangles, Parallelograms, Rhombus, and Trapezoids Mr. Miller Geometry Chapter 10 Sections 1 and 2

  2. Area Area is the amount of surface space that a flat object has. Area is reported in the amount of square units.

  3. When you measure the amount of carpet to cover the floor of a room, you measure it in square units. ? Would the area of your bedroom or the area of your house be greater? ? You’re right! The area of your house is greater than the area of your bedroom.

  4. Lets find the area of this surface if each square is equal to one foot. Count the number of squares. 1 2 Area = 15 square feet 3 4 5 6 7 8 9 10 11 12 13 14 15

  5. Try this one! Count the number of green squares to determine the area of this surface. What is the area? 1 2 3 4 5 6 7 8 9 The area is equal to 9 square units.

  6. Perimeter Perimeter is the distance around the outside edge of a flat object. Perimeter is reported as a total number of linear units.

  7. When you measure the amount of wallpaper border to go around a room, you measure it in lengths. ? Would the perimeter of your bedroom or the perimeter of your house be greater? ? You’re right! The perimeter of your house is greater than the perimeter of your bedroom.

  8. Let’s find the perimeter of this surface if each square is equal to one foot. Count the number of sides. Perimeter = 24 feet

  9. Try this one! Count the number of sides to determine the perimeter of this flat object. The perimeter is equal to 12.

  10. Family A Family B Let’s do these problems together. Two neighbors build swimming pools. This is what the pools look like. Which family has the pool with the bigger swimming area?

  11. Family A Family B The area of Family A’s pool is? 8 square units. The area of Family B’s pool is? 7 square units Therefore, Family A has the pool with the bigger swimming area.

  12. Family A Family B Now look at those same two pools. Which family has more side panels of the pool to clean? The perimeter of Family A’s pool is 12 units long. The perimeter of Family B’s pool is 14 units long. Therefore, Family B has more side panels of the pool to clean.

  13. AREAS OF POLYGONS Which of the following areas are you trying to find? Parallelogram Triangle Trapezoid

  14. AREA OF A PARALLELOGRAM b h Welcome. Today you’re going to discover the formula for area of a parallelogram. Click to Continue

  15. AREA OF A PARALLELOGRAM b h To do this let’s cut the left triangle and… Click to Continue

  16. AREA OF A PARALLELOGRAM b h h slide it… Click to Continue

  17. AREA OF A PARALLELOGRAM h b h slide it…

  18. AREA OF A PARALLELOGRAM h b h slide it…

  19. AREA OF A PARALLELOGRAM h b h slide it…

  20. b h AREA OF PARALLELOGRAM …thus, changing it to a rectangle. What is the area of the rectangle?

  21. Congratulations!!! You Answered Correctly. Click to continue.

  22. AREA OF A PARALLELOGRAM b h Since the area of the rectangle and parallelogram are the same, just rearranged, what is the formula for the area of this parallelogram?

  23. Congratulations!!! You Answered Correctly. Click to continue.

  24. The next slide will take you into discovering the area of a triangle. Do you wish to continue? Yes No

  25. AREA OF A TRIANGLE Hello. You will now be discovering the formula for area of a triangle. h Click to Continue b

  26. ? ? b AREA OF A TRIANGLE Let’s divide the triangle so that we divide the height in two. Click to Continue

  27. ? ? b AREA OF A TRIANGLE Remember, we divided the height into two equal parts. Now take the top and rotate… Click to Continue

  28. AREA OF A TRIANGLE ? rotate… ?

  29. AREA OF A TRIANGLE ? rotate… ? b

  30. AREA OF A TRIANGLE ? rotate… ? b

  31. AREA OF A TRIANGLE ? rotate… ? b

  32. AREA OF A TRIANGLE ? ? rotate… b

  33. ? ? b AREA OF A TRIANGLE …until you have a parallelogram. How would you represent the height of this parallelogram?

  34. AREA OF A TRIANGLE ? ? ? ? b b Remember, you divided the height in two. Click to Continue

  35. AREA OF A TRIANGLE ? b What is the area of this parallelogram?

  36. Congratulations!!! You Answered Correctly. Click to continue.

  37. AREA OF A TRIANGLE The area of this triangle would be the same as the parallelogram. Therefore, the formula for the area of a triangle is… what? h b

  38. Congratulations!!! You Answered Correctly. Click to continue.

  39. The next slide will take you into discovering the area of a trapezoid. Do you wish to continue? Yes No

  40. AREA OF A TRAPEZOID Hi. Let’s derive the formula for the area for a trapezoid. Click to Continue

  41. AREA OF A TRAPEZOID h Remember, there are two different bases on a trapezoid. Click to Continue

  42. ? ? AREA OF A TRAPEZOID First divide the trapezoid horizontally so the height is divided in two. Click to Continue

  43. AREA OF A TRAPEZOID ? ? Remember, we divided the height in two. Now, rotate… Click to Continue

  44. AREA OF A TRAPEZOID ? ? rotate…

  45. AREA OF A TRAPEZOID ? ? …until, you have a parallelogram. Click to Continue

  46. ? AREA OF A TRAPEZOID How would you represent the height of the parallelogram?

  47. ? ? ? AREA OF A TRAPEZOID Remember, we divided the height in two. Click to Continue

  48. ? AREA OF A TRAPEZOID How would you represent the base of the parallelogram?

  49. ? ? ? AREA OF A TRAPEZOID The new base is made by connecting the top and bottom bases. Click to Continue

  50. ? AREA OF A TRAPEZOID How would you represent the area of this parallelogram?

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