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**Lesson 8.1: Perimeter and Circumference**

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**Perimeter is the distance around a geometric figure**

Perimeter is the distance around a geometric figure. To find the perimeter P of a polygon, you can add the lengths of its sides. Find the perimeter. 25 cm 25 cm 15 cm

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**Find the perimeter of the polygon.**

20 cm 25 cm 30 cm

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**Find the perimeter of a rectangle.**

14 ft 18 ft P = 2l + 2w

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Check It Out: Example 2 Find the perimeter of a rectangle. 16 ft 8 ft

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

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

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**Find the circumference of the circle to the nearest tenth. Use 3**

Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = d 12 in.

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**Additional Example 3B: Finding the Circumference of a Circle**

Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r 18 cm

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Check It Out: Example 3A Find the circumference of the circle to the nearest tenth. Use 3.14 for . 7 in.

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Check It Out: Example 3B Find the circumference of the circle to the nearest tenth. Use 3.14 for . 11 cm

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**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 for . 22 7

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**for . Check It Out: Example 4**

The diameter of a circular spa is 14 m. What is its circumference? Use 22 7 for .

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**3. What is the circumference of a circle with a **

Lesson Quiz Find the perimeter. 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? Use for . 22 7

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**Lesson Quiz for Student Response Systems**

3. What is the circumference of a circle with a radius of 13 in.? Use 3.14 for . A in. B in. C in. D in. 14

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**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 15

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**Lesson 8.2: Area of a Polygons**

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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.

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

Find the area of the rectangle. A = lw

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

Find the area of the parallelogram.

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Check It Out: Example 1A Find the area of the rectangle. 6.3 in. 8.2 in.

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Check It Out: Example 1B Find the area of the parallelogram. 6 cm 12 cm

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**Find the area of the triangle.**

1 2 A = bh

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**Additional Example 2B: Finding the Area of a Triangle**

Find the area of the triangle.

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Check It Out: Example 2A Find the area of the triangle. 9 6

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Check It Out: Example 2B Find the area of the triangle. 10 7

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**The two parallel sides of a trapezoid are its bases, b1 and b2**

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.

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**In the term b1, the number 1 is called a subscript**

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

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**Additional Example 3A: Finding the Area of a Trapezoid**

Find the area of the trapezoid. 1 2 A = h(b1 + b2)

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**Additional Example 3B: Finding the Area of a Trapezoid**

Find the area of the trapezoid.

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**Find the area of the trapezoid.**

Check It Out: Example 3A Find the area of the trapezoid. 11 in. 4 in. 6 in.

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Check It Out: Example 3B Find the area of the trapezoid. 1 2 A = h(b1 + b2) Use the formula. 16 cm 1 2 A = · 9(5 + 16) Substitute. 9 cm 1 2 Add. 5 cm A = · 9(21) A = 94.5 Multiply. The area of the trapezoid is 94.5 cm2.

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**Lesson Quiz for Student Response Systems**

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 33

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**Find the area of each figure. 1. 2.**

Lesson Quiz Find the area of each figure. 28 1 2 ft2 57 or 24.5 ft2 45 ft2 9 in2 60 ft2 87.5 ft2

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**Lesson Quiz for Student Response Systems**

1. Identify the area of the rectangle. A cm2 B cm2 C cm2 D. 81 cm2 9 cm 5.3 cm 35

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**Lesson Quiz for Student Response Systems**

2. Identify the area of the parallelogram. A. 144 in2 B. 72 in2 C. 50 in2 D. 25 in2 36

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**Lesson Quiz for Student Response Systems**

3. Identify the area of the triangle. A. 48 cm2 B. 20 cm2 C. 36 cm2 D. 96 cm2 37

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**Lesson 8.3: Area of a Circle**

Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 7 cm

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

The order of operations calls for evaluating the exponents before multiplying. Remember! Find the area of the circle to the nearest tenth. Use 3.14 for . A = r2 18 ft

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

Check It Out: Example 1A Find the area of the circle to the nearest tenth. Use 3.14 for . 10 cm

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

Check It Out: Example 1B Find the area of the circle to the nearest tenth. Use 3.14 for . 12 ft

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**Park employees are fitting a top over a circular drain in the park**

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 22 7 for .

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**Albert was designing a cover for a spa**

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

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**Find the area of the shaded region of the circle. Use 3. 14 for **

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

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Check It Out: Example 3 Find the area of the shaded region of the circle. Use 3.14 for . Round your answer to the nearest tenth. 2.4 cm The measurement of the radius of the circle is 2.4 cm.

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**Find the area of each circle, to the nearest tenth. Use 3.14 for . 1.**

Lesson Quiz Find 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 is the area of the tablecloth? Use 3.14 for . Round your answer to the nearest tenth. 8 ft 2. 9 ft • •

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**Lesson Quiz for Student Response Systems**

1. Identify the area of the circle to the nearest tenth. Use 3.14 for . A ft2 B. 289 ft2 C ft2 D ft2 17 ft 47

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**Lesson Quiz for Student Response Systems**

2. Identify the area of the circle to the nearest tenth. Use 3.14 for . A in2 B in2 C in2 D in2 23 in. 48

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**Lesson Quiz for Student Response Systems**

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 ft2 C ft2 D. 34 ft2 49

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