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Appendix
Table of Contents
Assessments
Pre-Assessment....................................................................................................2
Area of Two-dimensional Figures.......................................................................4
Area of Two-dimensional Figure problem..........................................................6
Apothem.............................................................................................................10
Computing Surface Area....................................................................................12
Computing Volume (Craft time).........................................................................14
Density................................................................................................................16
Trigometric Ratios..............................................................................................18
Resources
Practice with nets................................................................................................22
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Name___________________________________________________Date____________________
Pre-assessment Activity
Answer the questions on a separate piece of paper.
Playground Reassessment Task
1) Use as many geometric terms as you can to describe this playground.
2) If you were planning to build this playground or one like it what would the floor plan look like?
Draw a quick sketch of this playground or one you would design on 8 x11 inch paper. (Imagine what
the playground would look like if you were a bird looking down on it.)
3) If you were convincing the town to build a playground, what type of information would you need to
know? What information would you present to the town board?
4)If the area allotted to construction the playground is a rectangle that is 14feet long and 20 feet wide,
what is the total area allotted to the playground in square feet?
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5)A wading pool has a diameter of three 4 feet. What is the total area of the wading pool?
Geometric terms
Altitude
base
sphere
circumference
composite figure
cone
cross section
cylinder
edge
face
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Circle
height
hemisphere
lateral area
lateral faces
oblique cylinder
oblique prism
polyhedron
prism
pyramid
radius
Regular pyramid
right cone
right cylinder
right prism
similar solids
slant eight
surface area
vertex volume
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Assessment Area of Two – Dimensional Problems
Answer key
1) [D] 24 feet
2) 252 square inches
3) $6.00
4) 38 inches
5) a) 18.84 feet
b) 28.23msquare feet
6) The circumference; the height is 3d, where d
is the diameter of the tennis ball, but the
circumference is approximately 3.14d.
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Date_________________________
Assessment Area of Two-dimensional Figures
Formative Assessment Area Problem solving
Problem 1
Roni and Terry will be sharing an apartment. For the living room Roni is bringing
a rectangular rug and Terry will bring a cylindrical ottoman. Roni’s rug
measures 48 inches by 42 inches. Terry’s ottoman has a diameter of 2
feet.
If the roommates place the ottoman in the center of the rug
how much of Roni’s rug will be visible? Terry says that they will be able to see 10% of the
rug.
Is Terry correct? If Terry is wrong explain what Terry may have done wrong.
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Name_____________________________
Date_________________________
Answer Key-Assessment Area of Two-dimensional Figures
Formative Assessment Area Problem solving
Problem 1
Roni and Terry will be sharing an apartment. For the living room Roni is bringing
a rectangular rug and Terry will bring a cylindrical ottoman. Roni’s rug
measures 48 inches by 42 inches. Terry’s ottoman has a diameter of 2
feet.
If the roommates place the ottoman in the center of the rug
how much of Roni’s rug will be visible? Terry says that they will be able to see 10% of the
rug.
Is Terry correct? If Terry is wrong explain what Terry may have done wrong.
Answer
Area of the rug: Area of rectangle= l * w 42 * 48 = 2016 square inches
Area of ottoman: Area of circle is Πr2 = Π(12)2= 452.4 square inches
452.4 =
7
x
=
22.4%
Actually Terry is wrong. 77.6% of the rug will show. Maybe
2016
8
100
Terry confused the feet and inches.
Name_____________________________
Geometry 2009 ed. p.537
Note: This problem is taken from Prentice Hall
Problem 2
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Name _________________________
Date ____________
Area of a regular polygon
1. The apothem of a regular polygon is the height of a triangle between the center and two
consecutive vertices of the polygon.
a.
Name the center and radius of the circle. Name the apothem of the polygon:
b. A = ½ ap is the formula used to find the area of a polygon, where a represents the apothem
and p represents the perimeter of the apothem. If one side length of the hexagon is 7 in. and
the length of the apothem is 4 in., find the area of the hexago
c.
d. Verify the area of the hexagon by finding the sum of the areas of each triangle of the
hexagon.
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e. Name _________________________
Date ____________
Area of a regular polygon
The apothem of a regular polygon is the height of a triangle between the center and two
consecutive vertices of the polygon.
Name the center and radius of the circle. Name the apothem of the polygon:
Center: O
Radius: OG
Apothem: OG
A = ½ ap is the formula used to find the area of a polygon, where a represents the apothem
and p represents the perimeter of the apothem. If one side length of the hexagon is 7 in. and
the length of the apothem is 4 in., find the area of the hexagon.
A = ½* 4 (7*6)= 84
Verify the area of the hexagon by finding the sum of the areas of each triangle of the
hexagon.
Area of one triangle = ½* 4* 7= 14
Area of 6 triangles = 6*14- 84
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Name __________________
Date___________________________
Surface Area Assessment
Assessment- Surface area of three-dimensional Figures
Amber is painting props for the school play.
If one can of paint covers 50 square feet how many cans of paint does Amber need to paint the figures
shown here? Round all answers to the nearest tenth.
Note: Amber was told the figures would be moved around so she must paint all faces including the
bottoms.
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Circular Cone Surface Area
• Total Surface Area
= L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
Object 1
πr(s + r)
=π(1.5)(4 + 1.5) = 25.9 ft2
Calculations for a rectangular prism:
Surface area = 2(lw + lh + wh)
= 2(5)(4) + 2(5)(3) +2(3)(4)
= 40 + 30 +24
= 94ft2
Object 3
Cylinder Calculations:
Object 4
• Total surface area of a closed cylinder is:
• A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)
=2π2.5(3+2.5)
= 86.425.9 ft2 +
14
Object 2
Amber needs 25.9 ft2 +94 ft2 +86.4 ft2 = 206.3 ft2 of paint.
206.3 / 50 = 4.1 Amber will buy 5 cans of paint even though she might get away with 4, she doesn't
want to run out.
Name__________________________
Date_________________________
Assessment -Volume
Craft Time
Here are some craft ideas.
(And you do have to solve the math as well- since this really is an assessment!)
1) Make a bird feeder
The cylindrical container that tennis balls comes in makes an excellent bird feeder. What is the volume
of the tennis canister that is 3 inches in diameter and 9 inches tall.
2) They ate- now the birds need some place to live.- Build a bird house.
The bird house is made up of a wooden box. The bottom of the box is a rectangular prism. The
dimensions of the rectangular prism are 12 inches by 6 inches by 8 inches. The roof is a triangular
prism. The dimensions of the roof (triangular prism are shown below. The triangular prism is placed
on top of the rectangular prism.. What is the volume of the bird
house?
.
3)Now a place to bathe.
The bird bath is made from an old globe cut in half. The radius is of the sphere is 9 inches. What is
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the volume if the bird bath? (Just the bowl part)
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Name__________________________
Date_________________________
Assessment -Volume
Craft Time
Here are some craft ideas.
(And you do have to solve the math as well- since this really is an assessment!)
1) Make a bird feeder
The cylindrical container that tennis balls comes in makes an excellent bird feeder. What is the volume
of the tennis canister that is 3 inches in diameter and 9 inches tall.
πr2h
where r = radius, h = height
Π(1.5)29 =63.6
2They ate- now the birds need some place to live.- Build a bird house.
The bird house is made up of a wooden box. The bottom of the box is a rectangular prism. The
dimensions of the rectangular prism are 12 inches by 6 inches by 10 inches. The roof is a triangular
prism. The dimensions of the triangular base are shown below. The triangular prism is placed on top
of the rectangular prism so the height of the prism (in this case the
edge that is on the side of the bird house) is 10 inches. What is the
volume of the bird house?
Volume of bottom part
V
H*W*L= 12*6*8= 576 square inches
Volume of the “roof”
½ H*W*L= 10*6*8 = 240 square inches
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Total volume 576 + 240 = 816 square
inches
3)Now a place to bathe.
The bird bath is made from an old globe cut in half. The radius is of the sphere is 9 inches. What is
the volume if the bird bath? (Just the bowl part)
Volume of a sphere
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Volume = 4/3 Π r3
4/3 Π (9)3
V = 3053.63 inches3
It is a hemisphere so the 3053.6 = 1526.6
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Name______________________________
Date_______________________________
Assessment Density
Marcos wants to buy a goldfish tank. He reads the following information in a fish tank advice book.
Since goldfish get their oxygen from the surface, you want a tank with a big surface.*** . The
number of gallons is not nearly as important as the surface area of the exposed face .For every
inch of fish length, you must have 30 sq inches of surface area. But remember! Your fish will also
grow, and you want to take this into account when choosing your tank.
The author of the fish tank advice
***
book calls this top face the
Marcos thinks like a mathematician and that sentence confused him. What the author
of fish tank
“surface”
advice book calls the surface is the top face of the rectangular prism.
Marcos has a choice of the following fish tanks
Fish Tank One:
A rectangular prism: 18inches high by 10 inches wide and 10 inches long
Fish Tank Two :
A rectangular prism: 15 inches high by 12 inches wide and 18 inches long
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This is what the water would look like in
the tank
Fish Tank Three:
A cylinder with a radius of 7 inches and a height of 16 inches
Which tank should Marcos buy? Why?
Answer Key
In order to determine how many fish you can safely keep in a container, you must find the surface area
of water that is exposed to the air. This is the top face of the three-dimensional figure that is your
tank. Don't forget that your goldfish will grow! The following formula works if the top of your tank is
rectangular. Be sure to count the goldfish's tail when considering how many inches of fish you have.
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Surface Area of face of water exposed to air = length * width
Inches of goldfish tank will support = Surface Area / 30
Example 1
Your tank is 18 inches long, 10 inches wide, and ten inches high. If we multiply the length (18) by the
width (10) we come up with 180 square inches of surface area (for the top surface of the water). Since
we need 30 square inches of surface area for each inch of fish, we can keep 6 inches of fish. So we
could keep 6 one-inch fish in this tank. Or 3 two-inch fish in this tank. Or 2 three-inch fish. Or any
combination that adds up to six inches.
example 2
An 18 gallon tank has the following measurements: Length is 24 inches. Width is 12 inches. Height is
15 inches. The surface area of the exposed face is 288 square inches (24 X 12). Divide by 30 (and
round down) to get nine inches of fish.
example 3
If your tank is a cylinder The diameter is 14 inches and the height is 16 inches
Surface Area of the exposed face = π r2 h = 72 * π = 153.86
153.86/30 = 5 fish
Adapted from: http://www.csh.rit.edu/~tonyl/goldfish/testarea/examples.htm
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Name ___________________________________
Class __________
Date ___________
Geometry Formative Assessment – Trigonometry
2. Write down the Sine, Cosine, and Tangent ratios.
3. Use the accompanying diagram of
a) Sin A
d) Sin B
b) Cos A
e) Cos B
to find the following ratios:
c) Tan A
f) Tan B
4. An 8-foot ramp leaning on a platform forms a 40 degree angle with the ground. Show the steps
to calculate the height of the platform.
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f.
Write down the Trigonometric ratio using x to represent the height of the platform.
g.
Solve for the height of the platform to the nearest tenth of a foot.
Name ___________________________________
Class __________
Answer Key
Geometry Formative Assessment – Trigonometry
5. Write down the Sine, Cosine, and Tangent ratios.
Sine = Opposite
Hypotenuse
Cosine = Adjacent
Hypotenuse
6. Use the accompanying diagram of
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b) Sin A= 13
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d) Sin B 13
Date ___________
Tan = Opposite
Adjacent
to find the following ratios:
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b) Cos A= 13
c) Tan A=
5
e) Cos B 13
12
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f) Tan B
5
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7. An 8-foot ramp leaning on a platform forms a 40 degree angle with the ground. Show the steps
to calculate the height of the platform.
h. Write down the Trigonometric ratio using x to represent the height of the platform.
i.
Solve for the height of the platform to the nearest tenth of a foot.
1
8 ft
Sine = Opposite
Hypotenuse
= X = 5.1
8
X
40
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