6-1 perimeter & area of rectangles & parallelograms course 3 warm up warm up problem of the...

6-1 Perimeter & Area of Rectangles & Parallelograms

Course 3

Warm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Bell Ringer 10-13Graph 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

Learn to find the perimeter and area of rectangles and parallelograms.

Course 3

Perimeter and Area of Rectangles and Parallelograms

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

units2 units2

A. (–1, –2), (2, –2), (2, 3), (–1, 3)

A = 15 units2

A = 3 • 5

A = bh

Additional Example 2A: Using a Graph to Find Area

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

Graph the figure with the given vertices. Then find the area of the figure.

Area of a rectangle.

Substitute 3 for b and 5 for h.

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

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

B. (0, 0), (5, 0), (6, 4), (1, 4)

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.

A = 20 units2

A = 5 • 4

A = bhArea of a parallelogram.

Substitute 5 for b and 4 for h.

Try This: Example 2A

A. (–3, –2), (1, –2), (1, 3), (–3, 3)

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

Graph the figure with the given vertices. Then find the area of the figure.

A = 20 units2

A = 4 • 5

A = bhArea of a rectangle.

Substitute 4 for b and 5 for h.x

y

(–3, –2) (1, –2)

(1, 3)(–3, 3)

4

5

B. (–1, –1), (3, –1), (5, 3), (1, 3)

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.

(5, 3)

x

y

(–1, –1) (3, –1)

(1, 3)

4

4

A = 16 units2

A = 4 • 4

A = bhArea of a parallelogram.

Substitute 4 for b and 4 for h.

5 533

6

Add the areas together.A = 6 • 5 + 6 • 2 + 6 • 5

= 30 + 12 + 30

= 72 units2

66

Additional Example 3 Continued

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

74

6

2

6

4

2

7 2

Find the area of the figure.

2

62

2

7

2 + 2

4

++

Add the areas together.

= 12 + 14 + 4 + 8

A = 2 • 6 + 7 • 2 + 2 • 2 + 4 • 2

= 38 units2

Try This: Example 3 Continued

2

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

2

Lesson Quiz: Part 1

1. Find the perimeter of the figure.

12 ft

12 ft

4 ft5 ft

5 ft

5 ft

5 ft

44 ft

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

Lesson Quiz: Part 2

2. Find the area of the figure.

108 ft2

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

12 ft

12 ft

4 ft5 ft

5 ft

5 ft

5 ft

Lesson Quiz: Part 3

Graph the figure with the given vertices and find its area.

50 units2

3. (–4, 2), (6, 2), (6, –3), (–4, –3)

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

Course 3

6-1 Perimeter & Area of Rectangles & Parallelograms

6-2 Perimeter and Area of Triangles and Trapezoids

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm Up

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft.

3. Find the area of a parallelogram with height 9 in. and base length 15 in.

2. Find the area of a rectangle with side lengths 24 in. and 32 in.

64 ft

768 in2

135 in2

Triangle: The area A of a triangle is one-half the base length b times the height h.

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

AREA OF A TRIANGLEAREA OF A TRIANGLEWords Numbers Formula

A = (8)(4)

= 16 units2

1 2

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

AREA OF A TRAPEZOIDAREA OF A TRAPEZOIDWords 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 = (2)(3 + 7)

= 10 units2

1 2

A = (h)(b1 + b2)

1 2

A. (–2, 2), (4, 2), (0, 5)

x

y

6

3

= 9 units2

A = bh12

Additional Example 2A: Finding the Area of Triangles and Trapezoids

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

(4, 2)

(0, 5)

(–2, 2)= • 6 • 31

2

Area of a triangle

Substitute for b and h.

B. (–1, 2), (5, –2), (5, 2), (–1, 6)

Additional Example 2B: Finding the Area of Triangles and Trapezoids

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

= 36 units2

A = h(b1 + b2)12

= • 6(8 + 4)12

Area of a trapezoid

Substitute for h, b1, and b2.

(–1, –2)

(–1, 6)

(5, 2)

x

y

(5, –2)

48 6

A. (–1, 1), (1, 7), (7, 1)

Try This: Example 2A

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

x

y

8

(1, 7)

(–1, 1) (7, 1)= 24 units2

A = bh12

= • 8 • 612

Area of a triangle

Substitute for b and h.6

B. (–2, –1), (0, 5), (3, 5), (5, –1)

(–2, –1)

(0, 5) (3, 5)

x

y

(5, –1)

3

7

6

Try This: Example 2B

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

= 30 units2

A = h(b1 + b2)12

= • 6(7 + 3)12

Area of a trapezoid

Substitute for h, b1, and b2.

Lesson QuizUse the figure to find the following measurements.

1. The perimeter of the triangle

2. The perimeter of the trapezoid

3. The perimeter of the combined figure

4. The area of the triangle

5. The area of the trapezoid

36 cm

44 cm

54 cm2

64 cm

104 cm2

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids