Warm Up

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## Warm Up

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**Warm Up**Problem of the Day Lesson Presentation Lesson Quizzes**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**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**Learn to find the perimeter and area of rectangles and**parallelograms.**Vocabulary**perimeter area**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.**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**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).**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**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**Check It Out: Example 1B**Find the perimeter of the figure. 5 13 P = 5 + 5 + 13 + 13 Add all side lengths. = 36 units**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.**Helpful Hint**The formula for the area of a rectangle can also be written as A = lw.**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**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**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**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**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.**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.**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**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**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**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 + + +**Lesson Quizzes**Standard Lesson Quiz Lesson Quiz for Student Response Systems**Lesson Quiz: Part I**1. Find the perimeter of the figure. 44 ft 108 ft2 2. Find the area of the figure.**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**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**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**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