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Understanding Perimeter and Area of Rectangles and Parallelograms

This lesson focuses on the concepts of perimeter and area for rectangles and parallelograms. Students will learn to calculate the perimeter by adding the lengths of all sides and to compute the area using the formulas A = base × height. Various examples, including practical problems like finding the perimeter of composite figures and using graphs to determine areas, will be provided. Additionally, students will explore problem-solving techniques and review vocabulary associated with the topic.

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Understanding Perimeter and Area of Rectangles and Parallelograms

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  1. Perimeter & Area of Rectangles & Parallelograms 6-1 Warm Up Problem of the Day Lesson Presentation Course 3

  2. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 • 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. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 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. Perimeter and Area of Rectangles and Parallelograms Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Learn to find the perimeter and area of rectangles and parallelograms. Course 3

  5. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Vocabulary perimeter area

  6. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 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. Perimeter & Area of Rectangles & Parallelograms 6-1 5 14 Course 3 Additional Example 1A: 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

  8. Perimeter & Area of Rectangles & Parallelograms 6-1 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. Course 3

  9. Perimeter & Area of Rectangles & Parallelograms 6-1 16 20 Course 3 Additional Example 1B: Finding the Perimeter of Rectangles and Parallelograms B. Find the perimeter of the figure. P = 16 + 16 + 20 + 20 = 72 units

  10. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Try This: Example 1A 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

  11. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Try This: Example 1B B. Find the perimeter of the figure. 5 13 P = 5 + 5 + 13 + 13 Add all side lengths. = 36 units

  12. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 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. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3

  14. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Additional Example 2A: 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

  15. Perimeter & Area of Rectangles & Parallelograms 6-1 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. Course 3

  16. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Additional Example 2B: 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

  17. Perimeter & Area of Rectangles & Parallelograms 6-1 y (–3, 3) (1, 3) x 5 4 (1, –2) (–3, –2) Course 3 Try This: Example 2A 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

  18. Perimeter & Area of Rectangles & Parallelograms 6-1 y (1, 3) (5, 3) x 4 (3, –1) 4 (–1, –1) Course 3 Try This: Example 2B 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

  19. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Additional Example 3: 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

  20. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Additional Example 3 Continued 6 6 3 3 6 5 5 A = 6 • 5 + 6 • 2 + 6 • 5 Add the areas together. = 30 + 12 + 30 = 72 units2

  21. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 Try This: Example 3 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

  22. Perimeter & Area of Rectangles & Parallelograms 6-1 2 4 7 2 6 2 2 2 Course 3 Try This: Example 3 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 + + +

  23. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 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

  24. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 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

  25. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 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

  26. Perimeter & Area of Rectangles & Parallelograms 6-1 Course 3 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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