GEOMETRIC FIGURES, AREAS,
AND VOLUMES
CHAPTER 7
NOTES PACKET 2009-2010
Geometric Terms (Day 1)
Point: _________________________________________________________________________________
Line: __________________________________________________________________________________
Plane: ________________________________________________________________________________
Line Segment: ________________________________________________________________________
Ray: __________________________________________________________________________________
Endpoint: _____________________________________________________________________________
Angle: ________________________________________________________________________________
Vertex: _______________________________________________________________________________
Perpendicular: ________________________________________________________________________
Parallel: ______________________________________________________________________________
Adjacent Angles: _____________________________________________________________________
Complementary Angles: ______________________________________________________________
Supplementary Angles: _______________________________________________________________
Linear Pair: ___________________________________________________________________________
Vertical Angles: _______________________________________________________________________
Transversal:
__________________________________________________
Alternate Interior Angles: ______________________________________________________________
Alternate Exterior Angles: ______________________________________________________________
Corresponding Angles: ________________________________________________________________
2
A
2
1
C
E
D
3
4
B
1 & 2 form a linear pair. 2 & 3 form a linear pair.
1. Going back to the definition, explain why they are linear pairs.
What makes 1 & 2 and 2 & 3 adjacent angles?
Which rays are opposite?
2. What other linear pairs are in this figure?
3. What seems to be the relationship between the angles of a linear pair?
4. Draw and give measures of:
 Two pairs of complementary angles:
 Two pairs of supplementary angles:
5. What kind of angle is the supplement of an acute angle? Right angle? Obtuse angle?
6. Looking back at the figure, is 1 supplementary to 2?
7. Name another angle that is supplementary to 1.
8. What do you notice about this angle and 2?
9. Are there any other vertical angles in the figure?
10. Is your discovery in question #8 true for all vertical angles?
11. Do you know anything about these angles’ complements? Supplements?
3
Try These!!!
1) The supplement of an angle is 40 more than the angle. Find the number of
degrees in the supplement.
2) Two complementary angles are the ratio of 7:2. Find the number of degrees in
each angle.
2
1
of the smaller is equal to
of the
3
2
result obtained when the larger is diminished by 20.
3) Find two complementary angles such that
4) RTM and NTS are vertical angles. If RTM equals (7x +16) and NTS equals
(3x + 48), find the number of degrees in each angle.
4
Angles and Parallel Lines (Day 2)
1) Label the transversal line t.
2) Identify all pairs of vertical angles. _______________________________________________
3) Identify all pairs of corresponding angles. ________________________________________
4) Identify all pairs of supplementary angles. ________________________________________
5) Identify all pairs of alternate interior angles. _______________________________________
6) Identify all pairs of alternate exterior angles. ______________________________________
7) Identify all linear pairs. ___________________________________________________________
5
Find the value of x.
What is the measure of CBA?
6
PERIMETER AND CIRCUMFERENCE (DAY 3)
VOCABULARY:
Polygon:
Regular Polygon:
Name
Number of Sides
of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
N-gon
Sum of Interior Angles
Measure of each Interior
Angle of Regular Polygon
Perimeter:
Ex1.
Find the perimeter of this polygon:
10 in
7 in
15 in
9 in
17 in
Ex2.
Find the perimeter of a rectangle that has a length of 4 meters and a width of 16
meters.
Ex3.
In the figure ABCD shown below, the total length of the sides equals 84 inches.
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Circumference:
EX1. Find the circumference of a circle with radius of 9 units:
a. in terms of 
b. to the nearest hundredth
EX2. Find the radius and diameter of a circle to the nearest tenth whose circumference
is 184 yards.
PERIMETER OF IRREGULAR SHAPES
EX1. Find the perimeter of the shape to the right.
15 cm
7 cm
5 cm
4 cm
4 cm
EX2. Erin is walking around a track like the figure below. Determine the distance around
the track.
a. in terms of 
150 ft
b. to the nearest hundredth
325 ft
8
AREA/SHADED REGION/IRREGULAR FIGURES (DAY 4)
VOCABULARY:
Area:
FORMULA FOR SHADED REGION
ASHADED REGION (ASR) =
FIGURE
NAME
AREA FORMULA
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EX1. Find the area of the figure.
13 cm
12 cm
EX2. Find the area of the figure.
30
25
40
EX3. The area of a trapezoid is 28 squared feet. The bases are 5 feet and 9 feet. What is
the height of the trapezoid in feet?
EX4. Jessica is making a circular tablecloth for an art project. She wants half of the cloth
to be a plain colored fabric and half to be a print fabric. How many square yards
of each fabric to the nearest hundredth will she actually be using if the diameter of
the cloth is 6 feet?
10
4
EX5. Find the area of the figure.
4
7
10
15
EX6. The diagram at the left shows a piece of square carpeting. A hole is being cut out
of the carpeting for a column 6' in diameter. How many square feet of carpeting
are shown in this diagram? Round answer to the nearest tenth of a square foot.
6 ft
18 ft
EX7. Find the number of square inches in the area of the shaded region of this square,
which is being intersected by two semicircles. Leave answer in terms of .
EX8. A 2 ft. wide sidewalk surrounds a 20 ft. by 15 ft. swimming pool. A fence on the
edge of the sidewalk encloses the whole pool area.
a. What is the area in square feet inside the fence?
b. What is the area in square feet of only the sidewalk?
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AREA OF FIGURES IN THE COORDINATE PLANE (DAY 5)
RECALL : Find the area of this figure. Express the answer to the nearest tenth.
RECALL: In the accompanying figure, square ABCD is circumscribed about circle O. The
length of a side of the square and the diameter of the circle are both 12.
A
B
a. What is the circumference of the circle in terms of ?
b. What is the perimeter of the square?
.O
c. What is the area of the square?
d. What is the area of the circle in terms of ?
D
C
e. What is the area of the shaded region of the diagram in terms of ?
PROCEDURE: AREA OF POLYGONS ON COORDINATE PLANE
METHOD 1: SIDES ARE PARALLEL TO THE AXES.
If the figure is drawn such that its sides (or needed segments) are drawn ON the
grids of your graph paper, you can COUNT the lengths and use your area
formulas.
METHOD 2: SIDES ARE NOT PARALLEL TO THE AXES.
If the figure is drawn such that its sides (or needed segments) are NOT drawn ON
the grids of your graph paper, you will need to draw a "BOX" around the figure to
determine its area
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EX1.
Find the area of triangle ABC given the coordinates A(-2, 1), B(2, 4), and C(4, 1).
EX2. Find the area of triangle ABC given the coordinates A(-3, 1), B(1, 3), and C(3, -2).
EX3. Find the area of ABCD given the coordinates A(-4, -2), B(-2, 2), C(2, 4), and D(4, -3).
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VOLUME OF SOLIDS (DAY 6)
VOCABULARY:
Volume:
Rectangular Solid (Prism):

Base:

Face:
Cube:
FORMULA FOR VOLUME OF RECTANGULAR SOLIDS
RECTANGULAR SOLID:
B = Area of the Base
h = height
s = side
CUBE:
EX1. Find the volume of the rectangular solid.
EX2. Find the volume of the cube.
7ft
14
EX3. If the volume of the prism below is 18,000 ft 3 ,
what is the value of x in inches?
EX4. If the cube shown below has a volume of 125 cm 3 ,
what is the length of a side of the cube?
CALCULATOR PROCEDURE FOR CUBE ROOTS
EX5.
1.
Press MATH 
2.
Enter number under
3.
Press Enter
3
option (choice 4)
3
sign.
The volume of a rectangular pool is 15,360 cubic meters. Its length, width, and
depth are in the ratio 10 : 6 : 4. Find the number of meters in each of the three
dimensions of the pool.
EX6. If the side of a cube is doubled, the volume is multiplied by:
(1) 6
(2) 2
(3) 8
(4) 4
EX7. If the length, width, and height of a rectangular solid are each doubled then the
volume of the original solid is multiplied by a factor of:
(1) 16
(2) 2
(3) 8
(4) 4
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VOLUME OF CYLINDERS (DAY 7)
VOCABULARY:
Right Circular Cylinder:
FORMULA FOR VOLUME OF CYLINDER
Cylinder Volume :
B = Area of the Base
h = height
r = radius
EX1. Find the volume of the cylinder, in terms of  .
EX2. Find the volume of the cylinder, to the nearest cubic foot.
14 ft
EX3. Find the height of a right circular cylinder that has a volume of 735  cm 3 and
a base radius of 7 cm.
EX4. The height of a cylinder is 16, and the area of the base is 25 squared units. Find in
cubic units the volume.
EX5. The cylindrical can containing food has a radius = 5 cm and a height = 12.5 cm. A
second cylindrical can of food has a radius of 6 cm and a height of 10 cm. If both
cans of food sell for the same price, which can is the better buy?
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SURFACE AREA OF RECTANGULAR SOLIDS AND CYLINDER (DAY 8)
VOCABULARY:
Surface Area:
FORMULA FOR SURFACE AREA OF RECTANGULAR SOLIDS
RECTANGULAR SOLID:
SA = surface area
l = length w = width
h=height s = side
CUBE:
EX1. Find the surface area of the rectangular solid if a = 7 mm.,
b = 9 mm. and c = 13 mm.
Find the volume of the rectangular prism.
EX2. Find the surface area of the cube.
Find the volume of the cube.
8 ft
EX3. If the surface area of a cube is 96cm2, what is the length of a side and what is the
volume of the cube?
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FORMULA FOR SURFACE AREA OF CYLINDERS
CYLINDER:
SA = surface area
h=height
s = side
EX1. Find, in terms of  , the surface area of the cylinder if a = 11 cm.
and b = 32 cm.
Find the volume, in terms of  , of the cylinder.
EX2. Find the surface area in terms of  of a cylinder when the diameter = 14 cm and
height = 5 cm.
EX3. A right cylinder is 8 inches high. The circumference of the base is 6 inches. Find
the surface area and volume of the right cylinder.
EX4. Given the formula: A = 2r2 + 2rh, solve for h in terms of A, r, and .
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