Download Camp 1 Lantern Packet

Kuta Software - Infinite Geometry
Name___________________________________
Angles and Their Measures
Date________________ Period____
Find the measure of each angle to the nearest degree.
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Worksheet by Kuta Software LLC
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Draw an angle with the given measurement.
11) 90°
12) 70°
13) 120°
14) 105°
15) 31°
16) 166°
17) 144°
18) 53°
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Worksheet by Kuta Software LLC
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Defining & Drawing Shapes
Find the definitions of each of the shapes below:
SquareRectangleTriangleRight triangleEquilateral triangle-
Draw a triangle below that has one angle that is 35° and one angle that is 45°.
Draw a square below that has 2.5 inch sides (use a ruler and a protractor).
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Draw a triangle below with 60° angles and 3 inch sides
Draw a rectangle below with 2 sides that are 3.75 inches long and two sides that are 5.25 inches long (use
a ruler and a protractor)
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Naming Polygons
Find the names of the following Polygons:
Polygon’s Name
Definition
A polygon with 3 sides
A polygon with 4 sides
A polygon with 5 sides
A polygon with 6 sides
A polygon with 7 sides
A polygon with 8 sides
A polygon with 9 sides
A polygon with 10 sides
A polygon with 12 sides
A polygon with 20 sides
Find the definition of a Regular Polygon:
Find the definition of an Interior Angle:
Shape #1 Triangle
Measure each of the
angles on the triangle to
the right. What is the
total (sum) of their
measurements?
Number of Sides
Total Degrees
Is this the same for all
triangles?
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Interior Angles of Polygons
Now using what you learned about the interior angle total (sum) of a triangle, prove the total angles of
these other polygons by dividing the shapes into the fewest number of triangles as possible. Use those
triangles to calculate the sums of the new shapes.
1. Lexi was solving the problems above when she noticed a pattern. “Aha”, she exclaimed, “the number of
triangles you can draw in each polygon is related to the number of sides of that polygon!”. Explain what
she means.
How can this be used to create a shortcut for finding the sum of the interior angles of any polygon?
2. Use Lexi’s discovery to find the sum of the interior angles of a regular polygon that has 8 sides.
3. How would you find the angle measurement of one of the angles in #2?
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Interior Angle Theorem
The sum of the interior angles of any polygon is equal to the number of sides of the polygon (n) minus
2 (this is the number of triangles in each polygon) then multiplied by 180 (the sum of the degrees
inside a triangle).
𝐼𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑠𝑢𝑚 = 𝑛 − 2 ∗ 180°
If the polygon is regular, you can find the measurement of each of the interior angles (if it is regular all
the angles will be the same) by dividing the interior angle sum by the number of sides (n).
𝑅𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑜𝑙𝑦𝑔𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 = 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 𝑠𝑢𝑚 ÷ 𝑛
4. Find the sum of the interior angles of a decagon.
5. Find the sum of the interior angles of a regular polygon that has 16 sides.
6. What is the measure of each angle of the regular polygon in #5?
7. Find the number of sides in a polygon whose sum of the interior angles is 1440.
8. Find the number of sides in a polygon whose sum of the interior angles is 1800.
9. What is the measure of each angle of the regular polygon in #8?
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10. Find the sum of the degree of the measures of the interior angles of a regular polygon that
has 13 sides.
11. What is the measure of one interior angle in the regular polygon in #10?
12. Find the number of sides in a polygon whose sum of the interior angles is 2700.
13. Find the sum of the degree measures of the interior angles of a regular polygon that has 15
sides.
14. What is the measure of one interior angle in the regular polygon in #13?
More Polygon Measurements
Complete the following problem with your group:
Dog Pen Problem: Ms. Mary got a new dog and wants to make the largest possible
pen for him. She has 60 feet of fencing. What is the largest area the pen can have?
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Before you move on to the next part of the packet, you must have your 6 recommended Khan Skills
mastered (out of this list…please follow the order below):
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Nets of 3D figures
Area of parallelogram
Area of triangle
Surface area using nets
Surface area
Area of composite shapes
Area of trapezoids
Area challenge
Volume 1
Volume with fractions
Volume with Unit Cubes
Volume Word Problems
Review…
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Putting it all together…The Lantern Project
Time to choose a polyhedron for your Lantern Project – Use the websites below to search through many
different polyhedron shapes. Once you have decided on the one you want, print out the net and fill in the
name of the polyhedron below.
http://www.senteacher.org/worksheet/12/NetsPolyhedra.html
http://www.korthalsaltes.com/
Name of the polyhedron you chose ___________________________________________________
Now that you have chosen your Polyhedron net for your lantern, you need to make some calculations to
determine how to enlarge your figure.
What is the total number of faces of your polyhedron? _________________
Your polyhedron is made up of one or more 2-dimensional polygons (such as a triangle, square, hexagon,
etc.) You will need to find the angle measurements and side lengths of each of these polygons. Use the space
below to record these measurements:
Name of Polygon 1 ________________________
Sum of interior angles of polygon 1 ___________________
Measurement of each angle ________________
(If polygon is regular, show calculation below. If not, carefully measure each angle)
Length of each side (list all lengths if they are not the same) ______________________________
Name of Polygon 2 ________________________
Sum of interior angles of polygon __________________
Measurement of each angle ________________
(If polygon is regular, show calculation below. If not, carefully measure each angle)
Length of each side (list all lengths if they are not the same) ______________________________
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Name of Polygon 3 ________________________ (if needed)
Sum of interior angles of polygon _________________
Measurement of each angle ________________
(If polygon is regular, show calculation below. If not, carefully measure each angle)
Length of each side (list all lengths if they are not the same) ______________________________
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Now it is time to see what your polyhedron will look like once it is completely constructed. Go ahead
and fold your net.
Diameter of your polyhedron ___________ (measure best you can from one side to the other)
Based on this diameter and the shape of your polyhedron, determine the scale factor for your enlarged
polyhedron. Remember that there will need to be enough space for a light bulb to fit inside.
Scale factor for lantern _____________
STOP
Before moving on you must get your scale factor approved by a teacher.
Teacher initials ________
ENLARGEMENT:
With your new measurements and your scale factor, you can begin to enlarge your polygons to provide you
with a template to use in construction. Use blank paper to precisely construct each polygon to the enlarged
size. You will turn these constructions in before you begin building.
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Surface Area Calculations
One more step before we begin our lamp construction. We need to calculate the total surface area of our
Polyhedron in order to estimate the tissue paper and ModPodge we will need for the construction. Use this
worksheet to calculate the surface area of each enlarged polygon in your polyhedron. Total up your values on
the bottom of the back page and give your teacher these results.
Name of Polygon #1 ________________________
Formula for calculating the surface area of this polygon __________________________________
Calculations:
How many faces of this polygon do you have in the polyhedron? __________
Total surface area of polygon #1:
_____________________ x __________________ = ___________________
surface area of polygon
# of faces
total surface area of polygon #1
-------------------------------------------------------------------------------------------------------------------------------------------------Name of Polygon #2 ________________________
Formula for calculating the surface area of this shape __________________________________
Calculations:
How many faces of this polygon do you have in the polyhedron? __________
Total surface area of polygon #2:
_____________________ x __________________ = ___________________
surface area of polygon
# of faces
total surface area of polygon #2
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Name of Polygon #3 ________________________ (if needed)
Formula for calculating the surface area of this polygon __________________________________
Calculations:
How many faces of this polygon do you have in the polyhedron? __________
Total surface area of polygon #3 (if needed):
_____________________ x __________________ = ___________________
surface area of polygon
# of faces
total surface area of polygon #3
-------------------------------------------------------------------------------------------------------------------------------------------------TOTAL
Total surface area
__________________+ ________________ + ________________ =
total surface area of #1
total surface area of #2
total surface area of #3
Congratulations! You are ready to begin building your lantern! Please turn in this packet and all extra
drawings/calculations to receive your Supplies Tracker and supplies.
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