Copyright © by Holt, Rinehart and Winston
Reteach
Developing Formulas for Circles and Regular Polygons
Find the circumference of circle S in which A ( 81( cm2.
Step 1 Use the given area to solve for r.
A ’ πr 2 Area of a circle
81π cm2 ’ πr 2 Substitute 81π for A.
81 cm2 ’ r 2 Divide both sides by π.
9 cm ’ r Take the square root of both sides.
Step 2 Use the value of r to find the circumference.
C ’ 2πr Circumference of a circle
C ’ 2π(9 cm) ’ 18π cm 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 π
[pic] [pic]
3. the area of circle Z in terms of π 4. the circumference of circle T in terms of π
[pic] [pic]
5. the circumference of circle X in 6. the radius of circle Y in which C ’ 18π cm
which A ’ 49π in2
Reteach
Developing Formulas for Circles and Regular Polygons continued
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
angle measure of a regular n-gon is [pic].
Step 2 Use the tangent ratio to find the apothem. You could also use the
30°-60°-90° ( Thm. in this case.
[pic] Write a tangent ratio.
[pic] Substitute the known values.
[pic] Solve for a.
Step 3 Use the formula to find the area.
[pic]
[pic] [pic] , P ’ 6 ( 10 or 60 cm
A ≈ 259.8 cm2 Simplify.
Find the area of each regular polygon. Round to the nearest tenth.
7. [pic] 8. [pic]
9. a regular hexagon with an apothem of 3 m 10. a regular decagon with a perimeter of 70 ft
4. [pic]
5. m∠K ’ tan−1[pic] 6. 35.5°
Problem Solving
1. 120 ft 2. 154 m
3. 57 ft 4. A
5. H 6. C
7. J
Reading Strategies
1. elevation 2. 21 m
3. 35 ft
Answers for Unit 3
Developing Formulas for Circles and Regular
Polygons
PRACTICE A
1. [pic]aP 2. πd
3. πr2 4. A ’ 25π ft2
5. A ’ 100π in2 6. C ’ 18π cm
7. C ’ 26π mi 8. 12 m
9. 2 km 10. 256π yd2
11. 314.2 in2; 530.9 in2; 572.6 in2
12. A ’ 27.6 ft2 13. A ’ 1086 mm2
14. s ’ 4 in.
Practice B
1. A ’ 625π m2 2. A ’ 4a2π in2
3. C ’ (2x + 2y)π yd 4. C ’ 1200π mi
5. r ( ( cm 6. d ( (2x ( 2) km
7. 353.0 mm2; 248.8 mm2; 471.4 mm2
8. 0.01 cent/mm2; 0.04 cent/mm2; 0.05 cent/mm2
9. the nickel
10. 2833 nickels; $141.65
11. A ≈ 1122.4 in2 12. A ≈ 85.6 m2
Practice C
1. Possible answer: By the definition of the center of a regular polygon,[pic], so (ABC is isosceles. By the Isosceles Triangle Theorem, ∠ACB ” ∠ABC. By the definition of apothem, ∠ADC and ∠ADB are right angles so ∠ADC ” ∠ADB by the Right Angle Congruence Theorem. [pic] by the reflexive property, so (ADC ” (ADB by AAS. By CPCTC, ∠CAD ” ∠BAD and [pic]. Thus, by the definition of angle bisector and segment bisector, [pic] bisects ∠BAC
and [pic].
2. A ≈ 2.828 units2; P ≈ 6.123 units
3. A ≈ 3.037 units2; P ≈ 6.231 units
4. A ≈ 3.139 units2; P ≈ 6.282 units
5. A ≈ 3.142 units2; P ≈ 6.283 units
6. The ratio of the perimeter to the area approaches 2.
7. Possible answer: As the number of sides in a regular polygon increases, the polygon gets closer to the shape of a circle, the distance from the center to a vertex gets closer to a radius, and the perimeter gets closer to a circumference. In a circle with a radius of 1 unit, the area is π units2 and the circumference is 2π units. So the ratio of the circumference to the area is 2.
8. 5 or 7
9. 3 10. 10
Reteach
1. C ’ 6 cm 2. A ’ 25π m2
3. A ’ 121π ft2 4. C ’ 20π in.
5. C ’ 14π in. 6. r ’ 9 cm
7. A ’ 695.3 cm2 8. A ’ 58.1 in2
9. A ’ 31.2 m2 10. A ’ 377.0 ft2
-----------------------
|Circumference and Area of Circles |
|A circle with diameter d and radius r has |
|circumference C ’ πd or C ’ 2πr. |
|A circle with radius r has area A ’ πr2. |
[pic]
|Area of Regular Polygons |
|The area of a regular |
|polygon with apothem |
|a and perimeter P |
|is [pic] |
The apothem is
the distance from
the center to a side.
The center is equidistant from the vertices.
[pic]
A central angle has its vertex at the center. This central angle measure is
[pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
Related searches
- cross technology winston salem
- rinehart 2 into 1 reviews
- holt science and technology pdf
- novant orthopedics winston salem
- holt science and technology worksheets
- quality education institute winston salem
- city of winston salem website
- city of winston salem nc
- winston salem journal
- holt and mcdougal online
- holt science and technology online
- holt science and technology answer key