Lesson 9-2 Devoloping Formulas for Circles and Regular Polygons

Topics: Regular polygon, Polygon, Circle Pages: 25 (3056 words) Published: January 3, 2013
Name
LESSON

Date

Class

Reteach
Developing Formulas for Circles and Regular Polygons
Circumference and Area of Circles

9-2

A circle with diameter d and radius r has circumference C d or C 2 r. A circle with radius r has area A 2 r .

Find the circumference of circle S in which A Step 1 Use the given area to solve for r. A 81 cm 2

2 81 cm .

r2 r r2 r
2

Area of a circle Substitute 81 for A. Divide both sides by . Take the square root of both sides. cm

81 cm2 9 cm Step 2

Use the value of r to find the circumference. C C 2 r 2 (9 cm) 18 cm Circumference of a circle Substitute 9 cm for r and simplify.

Find each measurement. 1. the circumference of circle B 2. the area of circle R in terms of

6 – cm

5m

C

6 cm

A

25 m2

3. the area of circle Z in terms of

4. the circumference of circle T in terms of

22 ft

10 in.

A

121 ft 2

C

20 in.
18 cm

5. the circumference of circle X in 2 which A 49 in

6. the radius of circle Y in which C

C

14 in.
14

r

9 cm
Holt Geometry

Name
LESSON

Date

Class

Reteach
Developing Formulas for Circles and Regular Polygons continued Area of Regular Polygons The center is equidistant from the vertices.

9-2

The area of a regular polygon with apothem a and perimeter P 1 is A __aP. 2

The apothem is the distance from the center to a side.

Find the area of a regular hexagon with side length 10 cm. Step 1 Draw a figure and find the measure of a central angle. Each central 360° angle measure of a regular n-gon is ____. n A central angle has its vertex at the center. This central angle measure is 360 ____ 60 . n Step 2 Use the tangent ratio to find the apothem. You could also use the 30°-60°-90° Thm. in this case. tan 30° tan 30° leg opposite 30° angle ____________________ leg adjacent to 30° angle 5 cm _____ Write a tangent ratio. Substitute the known values. Solve for a.

Step 3

a 5 cm a ______ tan 30° Use the formula to find the area. 1 A __ aP 2 A A 5 1 __ ______ 60 2 tan 30 259.8 cm 2

a

5 ______ , P tan 30°

6

10 or 60 cm

Simplify.

Find the area of each regular polygon. Round to the nearest tenth. 7. 12 cm

8.

4 in.

A

695.3 cm2 31.2 m2
15

A

58.1 in2 377.0 ft2
Holt Geometry

9. a regular hexagon with an apothem of 3 m

10. a regular decagon with a perimeter of 70 ft

A

A

Name
LESSON

Date

Class

Name
LESSON

Date

Class

Developing Formulas for Circles and Regular Polygons In Exercises 1–3, fill in the blanks to complete each formula. 1 __ aP 1. The area of a regular polygon with apothem a and perimeter P is A � 2 �d 2. A circle with diameter d has circumference C � . �r 2 3. A circle with radius r has area A � . Use the area and circumference formulas for circles to find each measurement. Give your answers in terms of �. 4. 5 ft

9-2

Practice A

9-2

Practice B
Developing Formulas for Circles and Regular Polygons
2.
25 m

.

1.

� 4� in.

the area of �V

the area of �H

5.

20 in. �

A � 625� m2
3.

(� � � ) yd

A � 4a 2� in2
4.

1200 mi

the area of �A

the area of �Q

A � 25� ft2
6.
� 18 cm

A � 100� in2
7.
13 mi

the circumference of �M

the circumference of �R

C � (2x � 2y)� yd
5. the radius of �D in which C � 2� cm
6. the diameter of �K in which A � (x � 2x � 1)� km 2 2
2

C � 1200� mi r � � cm
d � (2x � 2) km

the circumference of �W

the circumference of �N

C � 18� cm
8. the radius of �I in which A � 144� meters
2

9. the diameter of �L in which C � 2� kilometers
10. the area of �P in which C � 32� yards

C � 26� mi 12 m 2 km 256� yd2

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