Formulas for Areas of Polygons Coordinate Geometry Formulas

[Pages:16]Geometry B Exam Review The following formulas will be provided in the examination booklet:

Formulas for Areas of Polygons

Coordinate Geometry Formulas

Area of a Triangle: Area of a Rectangle: Area of a Trapezoid: Area of a Parallelogram: Area of a Regular Polygon:

Circle Formulas Area of a Circle:

Slope:

Distance:

Midpoint:

Right Triangles

B c

a

C b

A

Circumference of a circle:

Arc Length of a Circle:

Area of a Sector of a Circle:

Area of a Segment of a Circle: Area of sector ? Area of triangle

Angle and Arc Formulas:

Special Right Triangles

45o

a

45o

a

2a 30o

60o

a

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Geometry B Exam Review The following formulas will be provided in the examination booklet:

Formulas for Volume (V) and Surface Area (SA)

Right Prism V Bh area of base height

SA 2B Ph 2 area of base + perimeter height

Right Circular Cylinder

V Bh area of base height = r2h

SA 2B Ch 2 base circumference height 2 r2 2 rh

Right Pyramid

V

1 3

Bh

1 3

area of base height

SA

B

1 2

Pl

area of base +

1 2

perimeter of base slant height

Right Cone

V

1 3

Bh

1 3

area

of

base

height =

1 3

r

2

h

SA r2 rl

Sphere

V

4 3

r

3

SA 4 r2

Other Formulas

Diagonal of a Prism

D L2 W 2 H 2

Geometric Mean of Two Numbers

ab

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Geometry B Exam Review

For items 1 through 3, determine the area of the following composite figures. If the figure

is shaded, find the area of the shaded portion of the figure.

Note: Figures NOT drawn to scale

1.

2.

12 cm 20 cm 16 in

16 in

16 in

3. OR and OS are radii

R

8 ft

S

O

8 ft

16 in

For items 4 and 5, determine the probability that a dart will hit the shaded area of the target.

4.

3 in 6 in

Note: Figure NOT drawn to scale

A

1

4

5.

7 in

5 in

B

1

3

10 in

C

1

2

D

3

4

Note: Figure NOT drawn to scale

10 in

A

7

20

B

3

5

C

13

20

D

7

10

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Geometry B Exam Review

6. Which of the following statements are true?

a.

7 5 35

b.

35

5

7

c.

10 3 7

d.

5 6 11

e.

32 16 2 4 2

For items 7 through 9, determine the distance between the following pairs of points.

7. 2 ,6 and 5 ,9 8. 3 ,6 and 2 ,1 9. 1, 1 and 2 ,5

10. Given: Quadrilateral ROTS with vertices as labeled below.

Show that: If the midpoints of the sides of this quadrilateral are connected, then the figure formed has opposite sides that are congruent.

S(6,6) Q R(2,4)

M P

O(0,0)

N

T(8,0)

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Geometry B Exam Review

11. Given: Right triangle ABC with coordinates as shown. Point M is the midpoint of BC Find the area of triangle AMB C(0,6) M

A(0,0)

B(6,0)

For items 12 through 14, the lengths of three segments are given. State whether the triangle formed by the three segments is acute, right, or obtuse. Give reasons for your answers.

12. 6, 8, 10

13. 3, 8, 9

14. 9, 12, 14

For items 15 through 23, determine the value of x and/or y in each figure below.

Note: Figures NOT drawn to scale

15.

16.

10 x

7

4 x

7

17. 12

4

18.

y

3

45o x 15

x

19.

8

60o x

y

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Geometry B Exam Review 20.

x 45o

21.

30o x

y

22. x

12 45o

23.

y

30o

x

24. A regular hexagon has an area of 96 3 and an apothem of 4 3 . What is the length of each side of the hexagon?

A 2

B 4

C 8

D 83

For items 25 through 31, complete the information for each solid. Note: Figures NOT drawn to scale

25.

10

Surface Area: _______________

r = 6

Volume: ___________________

26.

A regular hexagon with perimeter = 36

and area =

12

Surface Area: ___________________

Volume: _______________________

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Geometry B Exam Review

27.

Point B is

Slant Height: _______________

4

at the center of

Surface Area: _______________

B

6 the square base.

Volume: ___________________

6

28. 4

r = 3 29.

4 cm

Slant Height: ________________ Surface Area: _______________ Volume: ____________________

Surface Area: _______________ Volume: ___________________

30. 9

10 5

31.

8

6

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Surface Area: _______________ Volume: ___________________

Surface Area: _______________ Volume: ___________________

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Geometry B Exam Review

32. If the radius of a sphere is doubled, what will happen to the surface area of the sphere?

A It will increase by a factor of 2. B It will increase by a factor of 4. C It will increase by a factor of 6. D It will increase by a factor of 8.

33. If each side of a cube is doubled, what will happen to the volume of the cube?

A It will increase by a factor of 2. B It will increase by a factor of 4. C It will increase by a factor of 6. D It will increase by a factor of 8.

34. Look at the right rectangular prism below.

C

E

D

G

7

A

3 F

B 5

a. What is the length of segment AE ? b. What is the relationship between diagonal AE and the prism?

35. A cube has a surface area of 24 in2. What is the volume of the cube?

36. In the figure below, the two cones are similar:

6

15

4

Note: Figures NOT drawn to scale

r

a. What is the value of r? Explain how you determined your answer. b. What is the ratio of the volumes of the cones? Explain how you determined your

answer.

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