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 Bell Ringer 10-13 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) 7 units 3 units 5 units

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

Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms units2

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 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

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 Exit Slip 10-13 Course 3 6-1 Perimeter & Area of Rectangles & Parallelograms Exit Slip 10-13 Graph the figure with the given vertices and find its area. 4. (4, –2), (–2, –2), (–3, 5), (3, 5) 42 units2

6-2 Warm Up Problem of the Day Lesson Presentation Perimeter and Area of Triangles and Trapezoids 6-2 Warm Up Problem of the Day Lesson Presentation Course 3

Course 3 6-2 Perimeter and Area of Triangles and Trapezoids Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 64 ft 2. Find the area of a rectangle with side lengths 24 in. and 32 in. 768 in2 3. Find the area of a parallelogram with height 9 in. and base length 15 in. 135 in2

6-2 AREA OF A TRIANGLE Words Numbers Formula Course 3 6-2 Perimeter and Area of Triangles and Trapezoids AREA OF A TRIANGLE Words Numbers Formula Triangle: The area A of a triangle is one-half the base length b times the height h. A = (8)(4) = 16 units2 1 2

6-2 AREA OF A TRAPEZOID Words Numbers Formula Course 3 6-2 Perimeter and Area of Triangles and Trapezoids AREA OF A TRAPEZOID Words Numbers Formula Trapezoid: The area of a trapezoid is one-half the height h times the sum of the base lengths b1 and b2. A = (h)(b1 + b2) 1 2 A = (2)(3 + 7) = 10 units2 1 2

Additional Example 2A: Finding the Area of Triangles and Trapezoids Course 3 6-2 Perimeter and Area of Triangles and Trapezoids Additional Example 2A: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. A. (–2, 2), (4, 2), (0, 5) Area of a triangle y A = bh 1 2 (0, 5) Substitute for b and h. = • 6 • 3 1 2 3 (–2, 2) (4, 2) 6 = 9 units2 x

Additional Example 2B: Finding the Area of Triangles and Trapezoids Course 3 6-2 Perimeter and Area of Triangles and Trapezoids Additional Example 2B: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. B. (–1, 2), (5, –2), (5, 2), (–1, 6) y (–1, 6) Area of a trapezoid A = h(b1 + b2) 1 2 (5, 2) Substitute for h, b1, and b2. 8 6 4 x = • 6(8 + 4) 1 2 (–1, –2) (5, –2) = 36 units2

6-2 Perimeter and Area of Triangles and Trapezoids Course 3 6-2 Perimeter and Area of Triangles and Trapezoids Try This: Example 2A Graph and find the area of the figure with the given vertices. A. (–1, 1), (1, 7), (7, 1) Area of a triangle y (1, 7) A = bh 1 2 Substitute for b and h. 6 = • 8 • 6 1 2 (7, 1) (–1, 1) = 24 units2 x 8

6-2 Perimeter and Area of Triangles and Trapezoids Course 3 6-2 Perimeter and Area of Triangles and Trapezoids Try This: Example 2B Graph and find the area of the figure with the given vertices. B. (–2, –1), (0, 5), (3, 5), (5, –1) y Area of a trapezoid 3 7 6 (3, 5) (0, 5) A = h(b1 + b2) 1 2 Substitute for h, b1, and b2. x = • 6(7 + 3) 1 2 (–2, –1) (5, –1) = 30 units2

6-2 Perimeter and Area of Triangles and Trapezoids Lesson Quiz Course 3 6-2 Perimeter and Area of Triangles and Trapezoids Lesson Quiz Use the figure to find the following measurements. 1. The perimeter of the triangle 36 cm 2. The perimeter of the trapezoid 44 cm 3. The perimeter of the combined figure 64 cm 4. The area of the triangle 54 cm2 5. The area of the trapezoid 104 cm2