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
MCPS ? 2012?2013
1
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
MCPS ? 2012?2013
2
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
MCPS ? 2012?2013
3
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)
MCPS ? 2012?2013
4
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
MCPS ? 2012?2013
5
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: _______________________
MCPS ? 2012?2013
6
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
MCPS ? 2012?2013
Surface Area: _______________ Volume: ___________________
Surface Area: _______________ Volume: ___________________
7
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.
MCPS ? 2012?2013
8
................
................
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
- math item specifications geometry
- guilford high school geometry syllabus
- geometry easy peasy all in one high school
- formulas for areas of polygons coordinate geometry formulas
- geometry labs activities for grades 8 11
- mathematics sample test high school 2010 2013
- calculator use in high school grades 9 12 math
- geometry a study guide credit by exam for ut high school
Related searches
- triangle geometry formulas calculator
- all geometry formulas pdf
- geometry formulas cheat sheet pdf
- geometry formulas pdf
- geometry formulas pdf free download
- basic geometry formulas pdf
- geometry formulas worksheets pdf
- all geometry formulas and equations
- geometry formulas cheat sheet
- area of polygons calculator
- geometry formulas for angles
- basic geometry formulas cheat sheet