Transcript Document

Lesson 8.1: Perimeter and
Circumference
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.
25 cm
20 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
The distance around a circle is called circumference.
For every circle, the ratio of circumference C to
diameter d is the same. This ratio, C , is
d
represented by the Greek letter , called pi. Pi is
approximately equal to 3.14 or 22 . By solving the
7
C
equation =  for C, you get the formula for
d
circumference.
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
Find the circumference of the circle to the
nearest tenth. Use 3.14 for .
18 cm
C = 2r
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
Helpful Hint
If the diameter or radius of a circle is a
22
multiple of 7, use for .
7
The diameter of a circular pond is 42 m. What
is its circumference? Use 22 for .
7
Check It Out: Example 4
The diameter of a circular spa is 14 m. What
is its circumference? Use 22 for .
7
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?
Use 22 for .
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. 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.
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.
A = 1 bh
2
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 height of a
trapezoid is the perpendicular distance
between the bases.
Reading Math
In the term b1, the number 1 is called a
subscript. It is read as “b-one” or “b sub-one.”
Additional Example 3A: Finding the Area of a
Trapezoid
Find the area of the trapezoid.
A = 1 h(b1 + b2)
2
Additional Example 3B: Finding the Area of a
Trapezoid
Find the area of the trapezoid.
Check It Out: Example 3A
Find the area of the trapezoid.
11 in.
6 in.
4 in.
Check It Out: Example 3B
Find the area of the trapezoid.
16 cm
9 cm
5 cm
A = 1 h(b1 + b2)
2
A = 1 · 9(5 + 16)
2
A = 1 · 9(21)
2
A = 94.5
Use the formula.
Substitute.
Add.
Multiply.
The area of the trapezoid is 94.5 cm2.
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
Lesson Quiz
Find the area of each figure.
1.
2.
57 or
2
28 1 ft2
2
24.5 ft2
3.
45 ft2
4.
5.
60 ft2
6.
9 in2
87.5 ft2
Lesson Quiz for Student Response Systems
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
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
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
Lesson 8.3: Area of a Circle
Find the area of the circle to the nearest tenth.
Use 3.14 for .
7 cm
A = r2
Remember!
The order of operations calls for evaluating the
exponents before multiplying.
Find the area of the circle to the nearest tenth.
Use 3.14 for .
A = r2
18 ft
Check It Out: Example 1A
Find the area of the circle to the nearest tenth.
Use 3.14 for .
10 cm
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. If the radius of the
drain is 14 inches, what is the area of the top
that will cover the drain? Use
22 for
7
.
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
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.
The measurement of the radius of the
circle is 2.4 cm.
2.4 cm
Lesson Quiz
Find the area of each circle, to the nearest
tenth. Use 3.14 for .
1.
8 ft
•
2.
9 ft
•
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.
Lesson Quiz for Student Response Systems
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
Lesson Quiz for Student Response Systems
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.
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. 69.1 ft2
C. 54.2 ft2
D. 34 ft2