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