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Think-Pair-share

Lesson 6.3 – Finding Perimeter and Area in the Coordinate Plane Concept : Distance in the Coordinate Plane EQ : how do we find area & perimeter in the coordinate plane? (g.gpe.7) vocabulary : distance formula, polygon, area, perimeter. Think-Pair-share.

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Think-Pair-share

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  1. Lesson 6.3 – Finding Perimeter and Area in the Coordinate PlaneConcept: Distance in the Coordinate PlaneEQ: how do we find area & perimeter in the coordinate plane? (g.gpe.7)vocabulary: distance formula, polygon, area, perimeter 6.2.2: Calculating Perimeter and Area

  2. Think-Pair-share • Think back to the distance formula and when you used it. Take a minute and write down everything you remember about using the distance formula. • With your partner, compare your notes to see if you missed anything. • Wait to be called on and then share your answers with the class. 6.2.2: Calculating Perimeter and Area

  3. Introduction • In the previous lesson, the distance formula was used to find the distance between two given points. In this lesson, the distance formula will be applied to perimeter and area problems. • Apolygonis a two-dimensional figure formed by three or more segments. We will use the distance formula to find the perimeter, or the sum of the lengths of all the sides of a polygon, and the area, the number of square units inside of a polygon, such as finding the amount of carpeting needed for a room. • Be sure to use the appropriate units (inches, feet, yards, etc.) with your answers. 6.2.2: Calculating Perimeter and Area

  4. Area of a Parallelogram • A parallelogramincludes shapes such as squares, rectangles, rhombuses. • The area of a parallelogram is found using the formula: Area = ) • The length of the base and height are found using the distance formula. • The final answer must include the appropriate label (units², feet², inches², meters², centimeters², etc.) 6.2.2: Calculating Perimeter and Area

  5. Guided practice, Example 1 • Parallelogram ABCDhas • vertices A (-5, 4), • B (3, 4), C (5, -1), and • D (-3, -1). Calculate the • perimeter and area of • parallelogram ABCD. 6.2.2: Calculating Perimeter and Area

  6. Example 1, continued • We need to find the length of all four sides before we can find the area and the perimeter. So we will use the distance formula: • The length of is 8 units 6.2.2: Calculating Perimeter and Area

  7. Example 1, continued • Distance formula: • The length of is 5.39 units 6.2.2: Calculating Perimeter and Area

  8. Example 1, continued • Distance formula: • The length of is 8 units 6.2.2: Calculating Perimeter and Area

  9. Example 1, continued • Distance formula: • The length of is 5.39 units 6.2.2: Calculating Perimeter and Area

  10. Example 1, continued • Find the perimeter by adding up all the sides: • Find the area by using the formula • or is the base and they are the same length so • The height can be found by drawing a perpendicularline straight up from D to side and down from B to side . • You can do this by counting the units or using the distance formula • Finding the distance from D to the point and the distance from B to the point where the perpendicular line touches at 6.2.2: Calculating Perimeter and Area

  11. Example 1, continued • Area of a Parallelogram = • Base = 8 units • Height = 5 units • Area of a parallelogram = 6.2.2: Calculating Perimeter and Area

  12. Area of a triangle • The area of a triangle is found by using the formula: Area = • The height of a triangle is the perpendicular distance from a vertex to the base of the triangle. • Determining the lengths of the base and the height is necessary if these lengths are not stated in the problem. • The final answer must include the appropriate label (units², feet², inches², meters², centimeters², etc.) 6.2.2: Calculating Perimeter and Area

  13. Guided practice, Example 2 • Triangle ABC has • vertices A (2, 1), • B (4, 5), and C (7, 1). • Calculate the perimeter • and area of triangle ABC. 6.2.2: Calculating Perimeter and Area

  14. Example 2 • We need to find the length of all three sides before we can find the area and the perimeter. So we will use the distance formula: • The length of is 4.47 units 6.2.2: Calculating Perimeter and Area

  15. Example 2, continued • Distance Formula: • The length of is 5 units. 6.2.2: Calculating Perimeter and Area

  16. Example 2, continued • Distance Formula: • 5 • The length of is 5 units. 6.2.2: Calculating Perimeter and Area

  17. Example 2, continued • Find the perimeter by adding up all the sides: • Find the area by using the formula • is the base so • The height can be found by drawing a perpendicularline straight down from B to side . • Then find the distance from B to the point where the perpendicular line touches at • You can do this by counting the units or using the distance formula 6.2.2: Calculating Perimeter and Area

  18. Example 2, continued • Area of a Triangle = • Base = 5 units • Height = the distance from to = 4 • Area of a triangle = 6.2.2: Calculating Perimeter and Area

  19. Area of a trapezoid • The area of a trapezoid is found by using the formula: Area = • A trapezoid has a smaller base () and a larger base () . You will need to add both bases together in the area formula. • The height of a trapezoid is the perpendicular distance from a vertex to the base of the trapezoid. • The final answer must include the appropriate label (units², feet², inches², meters², centimeters², etc.) 6.2.2: Calculating Perimeter and Area

  20. Guided practice, Example 3 • Trapezoid EFGH has • vertices E (-8, 2), • F (-4, 2), G (-2, -2), and • H (-10, -2). Calculate the • perimeter and area of • trapezoid EFGH. 6.2.2: Calculating Perimeter and Area

  21. Example 3, continued • We need to find the length of all four sides before we can find the area and the perimeter. So we will use the distance formula: • The length of is 4 units 6.2.2: Calculating Perimeter and Area

  22. Example 3, continued • Distance formula: • The length of is 4.47 units 6.2.2: Calculating Perimeter and Area

  23. Example 3, continued • Distance formula: • The length of is 8 units 6.2.2: Calculating Perimeter and Area

  24. Example 3, continued • Distance formula: • The length of is 4.47 units 6.2.2: Calculating Perimeter and Area

  25. Example 3, continued • Find the perimeter by adding up all the sides: • Find the area by using the formula • So . • The height can be found by drawing a perpendicularline straight down from E to side or from F to side . • You can do this by counting the units or using the distance formula 6.2.2: Calculating Perimeter and Area

  26. Example 3, continued • Area of a Trapezoid = • units • units • Height = 4 units • Area of a trapezoid = 6.2.2: Calculating Perimeter and Area

  27. You Try! • Find the perimeter and area of rectangleJKLM. • Reminder: Perimeter = sum of all the sides • Area = 6.2.2: Calculating Perimeter and Area

  28. 3-2-1 • 3 – List three things you learned from this lesson. • 2 – List two things you used in this lesson that you learned in previous lessons. • 1 – Write one question you still have about area and perimeter of polygons. 6.2.2: Calculating Perimeter and Area

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