Area & Circumference. Warm-Up Find each product. 1.) ½ · 122.) 20 · ½ 3.) ½ · 16 Evaluate...

Area & Circumference

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

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

Examples

Find the area of each parallelogram.1.) 4 CM 2.)

6 CM 10 cm

14 cm

Examples

Find the area of each triangle.3.) 4.)

15 in

10 in

8 in12 in

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.

Homework

Textbook pgs. 410-411 #1-22

A-Textbook pgs. 444-445 #2-14 Evens Only

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

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.

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)

Labeling the Trapezoid

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

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

Examples

4.) 5.)

Homework

Textbook pgs. 416-417 #1-13

Warm-Up

Simplify.1.) 1²

2.) 9²

3.) 11²

4.) 2 ∙ 3²

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

Example(s):

Find the circumference of each circle.1.) d = 10m 2.) r = 4in

3.) 4.)

Example(s):

Find the area of each circle.1.) r = 4cm 2.) d = 6ft

3.) 4.)

Classwork

Find the area and circumference of each circle.1.) d = 3in

2.) r = 2m

3.) d = 7ft

4.) r = 6km

5.) d = 8mi

Homework

Textbook pg. 422 #1-15

A-Textbook pg. 450 #1-18

Warm-up

Solve each of the following.1.) 4z = -24

2.) 33 = 3c

3.) 42 = 7f

4.) 3x + 5x = 48

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!