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 Pre-Algebra

Pre-Algebra 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

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

Learning Goal Assignment 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 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.

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

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

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

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

Try This: Example 1B B. 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 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.

units2

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

A = bh A = 4 • 5 A = 20 units2 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

The height of a parallelogram is not the length of its slanted side 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 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

A = bh A = 4 • 4 A = 16 units2 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 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 6 6 3 3 6 5 5 A = 6 • 5 + 6 • 2 + 6 • 5 Add the areas together. = 30 + 12 + 30 = 72 units2

Find the perimeter of the figure. 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 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 + + +

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

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

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

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