Lesson 8.1: Perimeter and Circumference

Find the perimeter.

25 cm25 cm

15 cm

Perimeter is the distance around a geometric figure. To find the perimeter P of a polygon, you can add the lengths of its sides.

20 cm25 cm

30 cm

Find the perimeter of the polygon.

Find the perimeter of a rectangle.

14 ft

18 ft

P = 2l + 2w

Check It Out: Example 2

Find the perimeter of a rectangle.

16 ft

8 ft

Cd

The distance around a circle is called circumference. For every circle, the ratio of circumference C to diameter d is the same. This ratio, , is

represented by the Greek letter , called pi. Pi is approximately equal to 3.14 or . By solving the 22

7equation = for C, you get the formula for circumference.

Cd

Find the circumference of the circle to the nearest tenth. Use 3.14 for .

12 in.C = d


Additional Example 3B: Finding the Circumference of a Circle

18 cmC = 2r


Check It Out: Example 3A

7 in.


Check It Out: Example 3B

11 cm

If the diameter or radius of a circle is a

multiple of 7, use for .

Helpful Hint

22 7

The diameter of a circular pond is 42 m. What is its circumference? Use 22

7for .

The diameter of a circular spa is 14 m. What is its circumference? Use


227

for .

Lesson Quiz

Find the perimeter.1. 2. a 10 in. by 8 in.

rectangle

3. What is the circumference of a circle with a a radius of 8 inches? Use 3.14 for . 4. If a guardrail is to be placed around the edge of a circular swimming pool with a diameter of 21 ft, how many feet of railing will be needed? 22

7Use for .

3. What is the circumference of a circle with a radius of 13 in.? Use 3.14 for .

A. 40.82 in.

B. 81.64 in.

C. 265.33 in.

D. 530.66 in.

Lesson Quiz for Student Response Systems

4. Jill plans to build a fence around her circular garden. About how many feet of fencing would be required if the garden has a diameter of 28 ft?

A. 88 ft

B. 66 ft

C. 44 ft

D. 22 ft


Lesson 8.2: Area of a Polygons

The area of a figure is the number of unit squares needed to cover the figure. Area is measured in units of length squared, or square units.

Find the area of the rectangle.

Additional Example 1A: Finding the Area of Rectangles and Parallelograms

A = lw

Find the area of the parallelogram.

Additional Example 1B: Finding the Area of Rectangles and Parallelograms

Find the area of the rectangle.

6.3 in.

8.2 in.


Find the area of the parallelogram.

6 cm

12 cm


Find the area of the triangle.

A = 12

bh


Additional Example 2B: Finding the Area of a Triangle



6

9



10

7

The two parallel sides of a trapezoid are its bases, b1 and b2. The height of a trapezoid is the perpendicular distance between the bases.

In the term b1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.”

Reading Math

Find the area of the trapezoid.

Additional Example 3A: Finding the Area of a Trapezoid

A = 12

h(b1 + b2)


Additional Example 3B: Finding the Area of a Trapezoid



4 in.6 in.

11 in.


A = 12

h(b1 + b2) Use the formula.

A = 12

· 9(5 + 16)

A =12

· 9(21)

A = 94.5

The area of the trapezoid is 94.5 cm2.

Substitute.

Multiply.

Add.


16 cm

5 cm

9 cm

Standard Lesson Quiz

Lesson Quizzes


Lesson Quiz

Find the area of each figure.

1. 2.

3. 4.

5. 6.

24.5 ft2

45 ft2

28 12

ft2

572

or

9 in2

60 ft2 87.5 ft2

1. Identify the area of the rectangle.

A. 28.09 cm2

B. 28.6 cm2

C. 47.7 cm2

D. 81 cm2


9 cm

5.3 cm

2. Identify the area of the parallelogram.

A. 144 in2

B. 72 in2

C. 50 in2

D. 25 in2


3. Identify the area of the triangle.

A. 48 cm2 B. 20 cm2

C. 36 cm2

D. 96 cm2


Lesson 8.3: Area of a CircleFind the area of the circle to the nearest tenth. Use 3.14 for .

7 cmA = r2

Find the area of the circle to the nearest tenth. Use 3.14 for .

18 ft

A = r2

The order of operations calls for evaluating the exponents before multiplying.

Remember!


10 cm



12 ft


Park employees are fitting a top over a circular drain in the park. If the radius of the drain is 14 inches, what is the area of the top that will cover the drain? Use

227

for .

Albert was designing a cover for a spa. If the radius of the spa is 7 ft, what is the area of the cover that will be made? Use

Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth.

The measurement of the radius of the circle is 1.5 cm.

1.5 cm

Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth.


The measurement of the radius of the circle is 2.4 cm.

2.4 cm

Lesson QuizFind the area of each circle, to the nearest tenth. Use 3.14 for .1.

3. The bull’s-eye on a target has a diameter of 2 in.What is the area of the bull’s-eye to the nearest tenth? Use 3.14 for . 4. A round tablecloth has a radius of 36 in. What isthe area of the tablecloth? Use 3.14 for . Roundyour answer to the nearest tenth.

2.8 ft 9 ft• •

1. Identify the area of the circle to the nearest tenth. Use 3.14 for .

A. 907.5 ft2

B. 289 ft2

C. 226.9 ft2

D. 53.4 ft2


17 ft

2. Identify the area of the circle to the nearest tenth. Use 3.14 for .

A. 72.2 in2

B. 144.4 in2

C. 415.3 in2

D. 1661.1 in2


23 in.

3. A round table has a diameter of 11 ft. What is the area of the table to the nearest tenth? Use 3.14 for .

A. 95 ft2

B. 69.1 ft2

C. 54.2 ft2

D. 34 ft2


Lesson 8.1: Perimeter and Circumference

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