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Warm Up

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.

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Warm Up

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  1. 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

  2. Perimeter & Area of Rectangles & Parallelograms 6.1 Pre-Algebra

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

  4. Vocabulary perimeter area

  5. 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.

  6. 5 14 Example: Finding the Perimeter of Rectangles and Parallelograms A. 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

  7. Helpful Hint The formula for the perimeter of a rectangle can be written as P = 2b + 2h, where b is the length of the base and h is the height.

  8. 16 20 Example: Finding the Perimeter of Rectangles and Parallelograms B. Find the perimeter of the figure. P = 16 + 16 + 20 + 20 = 72 units

  9. Try This A. 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

  10. Try This B. Find the perimeter of the figure. 5 13 P = 5 + 5 + 13 + 13 Add all side lengths. = 36 units

  11. 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.

  12. units2 units2

  13. Example: Using a Graph to Find Area Graph the figure with the given vertices. Then find the area of the figure. A. (–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

  14. Helpful Hint The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base.

  15. Example: Using a Graph to Find Area Graph the figure with the given vertices. Then find the area of the figure. B. (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) Try This Graph the figure with the given vertices. Then find the area of the figure. A. (–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) Try This Graph the figure with the given vertices. Then find the area of the figure. B. (–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. Example: 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

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

  20. Try This 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

  21. 2 4 7 2 6 2 2 2 Try This 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 + + +

  22. Lesson Quiz: Part 1 1. Find the perimeter of the figure. 12 ft 5 ft 5 ft 4 ft 5 ft 5 ft 44 ft 12 ft

  23. Lesson Quiz: Part 2 2. Find the area of the figure. 12 ft 5 ft 5 ft 4 ft 5 ft 5 ft 108 ft2 12 ft

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

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

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