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

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

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

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

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

Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms Any side of a rectangle or parallelogram can be chosen as the base. The height is measured along a line perpendicular to the base. Rectangle Parallelogram 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.

6-1 Perimeter & Area of Rectangles & Parallelograms Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms Additional Example 1A: Finding the Perimeter of Rectangles and Parallelograms A. Find the perimeter of the figure. 5 14 P = 14 + 14 + 5 + 5 Add all side lengths. = 38 units or P = 2b + 2h Perimeter of rectangle. Substitute 14 for b and 5 for h. = 2(14) + 2(5) = 28 + 10 = 38 units

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

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

6-1 Perimeter & Area of Rectangles & Parallelograms Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms Try This: Example 1A A. Find the perimeter of the figure. 6 11 P = 11 + 11 + 6 + 6 Add all side lengths. = 34 units or P = 2b + 2h Perimeter of rectangle. Substitute 11 for b and 6 for h. = 2(11) + 2(6) = 22 + 12 = 34 units

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

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

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

Additional Example 2A: Using a Graph to Find Area Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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

6-1 Helpful Hint Perimeter & Area of Rectangles & Parallelograms Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms The height of a parallelogram is not the length of its slanted side. The height of a figure is always perpendicular to the base. Helpful Hint

Additional Example 2B: Using a Graph to Find Area Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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

Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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) x y (–3, –2) (1, –2) (1, 3) (–3, 3) 4 5 Area of a rectangle. A = bh Substitute 4 for b and 5 for h. A = 4 • 5 A = 20 units2

Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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) (5, 3) x y (–1, –1) (3, –1) (1, 3) 4 Area of a parallelogram. A = bh Substitute 4 for b and 4 for h. A = 4 • 4 A = 16 units2

Additional Example 3: Finding Area and Perimeter of a Composite Figure Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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

Additional Example 3 Continued Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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

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

Try This: Example 3 Continued Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms 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 2 6 = 12 + 14 + 4 + 8 2 2 = 38 units2 2 6 4 2 4 7 2 2 + + +

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

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

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

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