Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a...
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Transcript of Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a...
![Page 1: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/1.jpg)
Area & Circumference
![Page 2: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/2.jpg)
Warm-Up
Find each product.1.) ½ · 12 2.) 20 · ½ 3.) ½ · 16
Evaluate if a = 3, b = 4, and c = 64.) abc 5.) ab ÷ 2
Solve for d using a = 3, b = 4, and c = 66.) cd = ab
![Page 3: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/3.jpg)
Area of Parallelograms and Triangles
The height of a parallelogram is the perpendicular distance from one base of a parallelogram to the other
To find the area of a parallelogram use:Area = base · height
Any side of a triangle can be considered the base of the triangle
The height of a triangle is the length of the perpendicular segment from a vertex to the base opposite the vertex
To find the area of a triangle use:Area = base · height ÷ 2
![Page 4: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/4.jpg)
Examples
Find the area of each parallelogram.1.) 4 CM 2.)
6 CM 10 cm
14 cm
![Page 5: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/5.jpg)
Examples
Find the area of each triangle.3.) 4.)
15 in
10 in
8 in12 in
![Page 6: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/6.jpg)
Example
5.) Determine the other length of a parallelogram that has a side length of 7 m and an area of 63 m².
6.) Determine the length of one side of square if the area is 64 in².
![Page 7: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/7.jpg)
Homework
Textbook pgs. 410-411 #1-22
A-Textbook pgs. 444-445 #2-14 Evens Only
![Page 8: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/8.jpg)
Warm-Up
Find the area of each parallelogram.1.) b = 10, h = 122.) b = 7, h = 13
Find the area of each triangle.3.) b = 10, h = 124.) b = 7, h = 13
![Page 9: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/9.jpg)
Warm-Up
A town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet. What will the area of the park be?
***Draw a picture first then solve.
![Page 10: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/10.jpg)
Area of Trapezoids & Other Figures
The two parallel sides of a trapezoid are the bases with lengths b1 and b2
The height h is the length of a perpendicular segment connecting the bases
The formula for the area of a trapezoid follows the formula for area of a parallelogram( A = bh)
Area of a Trapezoid: A = ½ · height(b1 + b2)
![Page 11: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/11.jpg)
Labeling the Trapezoid
![Page 12: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/12.jpg)
Examples
Find the area of each trapezoid.
1.)
2.) b1 = 4 in
b2 = 8 in
h = 5 in
3.) b1 = 11 in
b2 = 16 in
h = 8 in
10 m
12 m
8 m
20 m
![Page 13: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/13.jpg)
Finding area of other figures
To find the area of “other figures” or irregular figures, separate the figure into familiar figures(triangles, parallelogram, trapezoids)
Then find the area of each piece and add the areas together
![Page 14: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/14.jpg)
Examples
4.) 5.)
![Page 15: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/15.jpg)
Homework
Textbook pgs. 416-417 #1-13
![Page 16: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/16.jpg)
Warm-Up
Simplify.1.) 1²
2.) 9²
3.) 11²
4.) 2 ∙ 3²
![Page 17: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/17.jpg)
Circumference & Area of Circles
Circumference is the distance around a circle
To find circumference, use the formula:Circumference = π ∙ diameter or C = 2 ∙ π ∙ radius
To find the area of a circle, use the formula:Area = π ∙ radius²
*** π means pi(not “pie”) and it equals 3.14
![Page 18: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/18.jpg)
Example(s):
Find the circumference of each circle.1.) d = 10m 2.) r = 4in
3.) 4.)
![Page 19: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/19.jpg)
Example(s):
Find the area of each circle.1.) r = 4cm 2.) d = 6ft
3.) 4.)
![Page 20: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/20.jpg)
Classwork
Find the area and circumference of each circle.1.) d = 3in
2.) r = 2m
3.) d = 7ft
4.) r = 6km
5.) d = 8mi
![Page 21: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/21.jpg)
Homework
Textbook pg. 422 #1-15
A-Textbook pg. 450 #1-18
![Page 22: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/22.jpg)
Warm-up
Solve each of the following.1.) 4z = -24
2.) 33 = 3c
3.) 42 = 7f
4.) 3x + 5x = 48
![Page 23: Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate if a = 3, b = 4, and c = 6 4.) abc5.) ab ÷ 2 Solve for d using.](https://reader036.fdocuments.net/reader036/viewer/2022062716/56649dbf5503460f94ab2c57/html5/thumbnails/23.jpg)
Working Backwards?
***If you are given the circumference of a circle and you are to find the radius or diameter, think “backwards”
***work the problem backwards!