 # Lesson 8.1: Perimeter and Circumference

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Lesson 8.1: Perimeter and Circumference

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

Find the perimeter of the polygon.
20 cm 25 cm 30 cm

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

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.

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.

Additional Example 3B: Finding the Circumference of a Circle
Find the circumference of the circle to the nearest tenth. Use 3.14 for . C = 2r 18 cm

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

Check It Out: Example 3B Find the circumference of the circle to the nearest tenth. Use 3.14 for . 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 for . 22 7

for . Check It Out: Example 4
The diameter of a circular spa is 14 m. What is its circumference? Use 22 7 for .

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

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

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

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.

Additional Example 1A: Finding the Area of Rectangles and Parallelograms
Find the area of the rectangle. A = lw

Additional Example 1B: Finding the Area of Rectangles and Parallelograms
Find the area of the parallelogram.

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

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

Find the area of the triangle.
1 2 A = bh

Additional Example 2B: Finding the Area of a Triangle
Find the area of the triangle.

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

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

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.

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

Additional Example 3A: Finding the Area of a Trapezoid
Find the area of the trapezoid. 1 2 A = h(b1 + b2)

Additional Example 3B: Finding the Area of a Trapezoid
Find the area of the trapezoid.

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

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.

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

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

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

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

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

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

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

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

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

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 .

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

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

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.

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

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

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

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