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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up • Graph the line segment for each set of ordered pairs. Then find the length of the line segment. • 1. (–7, 0), (0, 0) • 2. (0, 3), (0, 6) • 3. (–4, –2), (1, –2) • 4. (–5, 4), (–5, –2) 7 units 3 units 5 units 6 units

  3. Problem of the Day Six pennies are placed around a seventh so that there are no gaps. What figure is formed by connecting the centers of the six outer pennies? regular hexagon

  4. Learn to find the perimeter and area of rectangles and parallelograms.

  5. Vocabulary perimeter area

  6. Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base. Parallelogram Rectangle Height Height Side Base Base Perimeter is the distance around the outside of a figure. To find the perimeter of a figure, add the lengths of all its sides.

  7. 5 14 Additional Example 1A: Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of the figure. Add all side lengths. P = 14 + 14 + 5 + 5 = 38 units Perimeter of rectangle. or P = 2b + 2h Substitute 14 for b and 5 for h. = 2(14) + 2(5) = 28 + 10 = 38 units

  8. Caution! When referring to the measurements of a rectangle, the terms length (l) and width (w) are sometimes used in place of base (b) and height (h). So the formula for the perimeter of a rectangle can be written as P = 2b + 2h = 2l + 2w = 2(l + w).

  9. 16 20 Additional Example 1B: Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of the figure. Add all side lengths. P = 16 + 16 + 20 + 20 = 72 units

  10. Check It Out: Example 1A Find the perimeter of the figure. 6 11 Add all side lengths. P = 11 + 11 + 6 + 6 = 34 units Perimeter of rectangle. or P = 2b + 2h Substitute 11 for b and 6 for h. = 2(11) + 2(6) = 22 + 12 = 34 units

  11. Check It Out: Example 1B Find the perimeter of the figure. 5 13 P = 5 + 5 + 13 + 13 Add all side lengths. = 36 units

  12. Area is the number of square units in a figure. A parallelogram can be cut and the cut piece shifted to form a rectangle with the same base length and height as the original parallelogram. So a parallelogram has the same area as a rectangle with the same base length and height.

  13. Helpful Hint The formula for the area of a rectangle can also be written as A = lw.

  14. Additional Example 2A: Using a Graph to Find Area Graph the figure with the given vertices. Then find the area of the figure. (–1, –2), (2, –2), (2, 3), (–1, 3) Area of a rectangle. A = bh Substitute 3 for b and 5 for h. A = 3 • 5 A = 15 units2

  15. Additional Example 2B: Using a Graph to Find Area Graph the figure with the given vertices. Then find the area of the figure. (0, 0), (5, 0), (6, 4), (1, 4) Area of a parallelogram. A = bh Substitute 5 for b and 4 for h. A = 5 • 4 A = 20 units2

  16. y (–3, 3) (1, 3) x 5 4 (1, –2) (–3, –2) Check It Out: Example 2A Graph the figure with the given vertices. Then find the area of the figure. (–3, –2), (1, –2), (1, 3), (–3, 3) Area of a rectangle. A = bh Substitute 4 for b and 5 for h. A = 4 • 5 A = 20 units2

  17. y (1, 3) (5, 3) x 4 (3, –1) 4 (–1, –1) Check It Out: Example 2B Graph the figure with the given vertices. Then find the area of the figure. (–1, –1), (3, –1), (5, 3), (1, 3) Area of a parallelogram. A = bh Substitute 4 for b and 4 for h. A = 4 • 4 A = 16 units2

  18. Additional Example 3: Estimating Area Using Composite Figures Use a composite figure to estimate the shaded area. Draw a composite figure that approximates the irregular shape. Divide the composite figures into simple shapes. Area of larger rectangle: A = bh =2 • 4 = 8 Area of smaller rectangle: A = bh =1 • 2.5 = 2.5 The shaded area is approximately 10.5 square units.

  19. Check It Out: Example 3 Use a composite figure to estimate the shaded area. Draw a composite figure that approximates the irregular shape. Divide the composite figures into simple shapes. Area of larger rectangle: A = bh =3 • 4 = 12 Area of smaller rectangle: A = bh =2 • 4 = 8 The shaded area is approximately 20 square units.

  20. Additional Example 4: Finding Area and Perimeter of a Composite Figure Find the perimeter and area of the figure. 6 6 3 3 6 5 5 The length of the side that is not labeled is the same as the sum of the lengths of the sides opposite, 18 units. P = 5 + 6 + 3 + 6 + 3 + 6 + 5 + 18 = 52 units

  21. Additional Example 4 Continued 6 6 3 3 6 5 5 A = 6 • 5 + 6 • 2 + 6 • 5 Add the areas together. = 30 + 12 + 30 = 72 units2

  22. Check It Out: Example 4 Find the perimeter of the figure. The length of the side that is not labeled is 2. 2 4 6 7 7 2 6 2 P = 6 + 2 + 4 + 7 + 6 + 4 + 2 + 2 + 2 + 7 ? = 42 units 4

  23. 2 4 7 2 6 2 2 2 Check It Out: Example 4 Continued 2 Find the area of the figure. 4 6 7 Add the areas together. A = 2 • 6 + 7 • 2 + 2 • 2 + 4 • 2 7 2 6 2 = 12 + 14 + 4 + 8 2 2 = 38 units2 4 + + +

  24. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  25. Lesson Quiz: Part I 1. Find the perimeter of the figure. 44 ft 108 ft2 2. Find the area of the figure.

  26. Lesson Quiz: Part II Graph the figure with the given vertices and find its area. 3. (–4, 2), (6, 2), (6, –3), (–4, –3) 50 units2

  27. Lesson Quiz: Part III Graph the figure with the given vertices and find its area. 4. (4, –2), (–2, –2), (–3, 5), (3, 5) 42 units2

  28. Lesson Quiz for Student Response Systems 1. Identify the perimeter of the figure. A. 34 feet B. 32 feet C. 30 feet D. 28 feet

  29. Lesson Quiz for Student Response Systems 2. Identify the area of the figure. A. 32 in2 B. 34 in2 C. 38 in2 D. 44 in2