Geometry
HS Mathematics
Unit: 08 Lesson: 01
Perimeter, Circumference, and Area KEY
Notes
The perimeter of a polygon is the total distance around a polygon. Although there are formulas for
finding the perimeter of a rectangle (2l + 2w) and for the square (4s), perimeter for any polygon can
be found by adding together the lengths of all the sides of the figure.
The circumference of a circle is the total distance around a circle. There are two formulas for finding
the circumference of a circle (d and 2r).
The area of polygons and circles is the surface covered within the figure. Formulas for the area of
polygons depend on the type of polygon. The formula for the area of a circle is always r 2.
Compare and contrast the formulas for perimeter, circumference, and area as they appear on the
Grades 9, 10, and Exit Level Mathematics Chart for TAKS and the Geometry STAAR Reference
Materials.
Grades 9, 10,
and Exit Level
Mathematics
Chart for
TAKS
Geometry
STAAR
Reference
Materials
Texas Education Agency. (2011). State of Texas Assessments of Academic Readiness: STAAR Geometry Reference Materials. Austin, TX: Author.
©2012, TESCCC
04/25/13
page 1 of 7
Geometry
HS Mathematics
Unit: 08 Lesson: 01
Texas Education Agency. (2007). Texas Assessment of Knowledge and Skills: TAKS Grades 9, 10, and Exit Level Mathematics Chart. Austin, TX: Author.
©2012, TESCCC
04/25/13
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Geometry
HS Mathematics
Unit: 08 Lesson: 01
Perimeter, Circumference, and Area KEY
Dimensional Change:
When one or more dimensions are changed non-proportionally:
• Perimeter must be recalculated using the new dimensions.
•
Area must be recalculated using the new dimensions.
When dimensions are changed proportionally:
• Perimeter is multiplied by the scale factor of the dimensions.
•
Area is multiplied by the square of the scale factor of the dimensions.
Practice Problems (Some answers are approximated and may vary depending on rounding
methods such as rounding along the way or at the end of calculations.)
Round answers to the nearest hundredth, when necessary.
Figure
Perimeter/Circumference
Area
1. Rectangle
24 cm
30 cm
84 cm
432 cm2
6 in.
Triangle
18 in
15.59 in2
26 m
26 m
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04/25/13
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Geometry
HS Mathematics
Unit: 08 Lesson: 01
24 m
25 m
Trapezoid
122 m
840 m2
©2012, TESCCC
04/25/13
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Geometry
HS Mathematics
Unit: 08 Lesson: 01
Perimeter, Circumference, and Area KEY
Figure
Perimeter/Circumference
Area
60o
16 ft
12 ft
Parallelogram
56 ft
166.28 ft2
26 m
18 m
32 m
Rhombus
128 m
936 m2
50 m
Circle
222.14 m
3,926.99 m2
Find the solution to the questions.
2. The Alice High School Ag department is constructing a garden area in the shape of an
isosceles trapezoid with legs of 15 feet and bases of 10 feet and 28 feet. They are going to
enclose the garden with chain length fencing. How many feet of fencing will the Ag department
need to purchase? If all the enclosed area can be utilized, how many square feet will be
available for planting?
Fencing: 68 ft
Planting Area: 228 ft2
©2012, TESCCC
04/25/13
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Geometry
HS Mathematics
Unit: 08 Lesson: 01
3. A petrochemical plant in Houston conducted a practice “Shelter in Place” for the residents
within a 3.2 mile radius. Warnings were sent to all residents to “Shelter in Place.” How many
square miles, to the nearest hundredth, had to “Shelter in Place”? How many square
kilometers, to the nearest hundredth, had to “Shelter in Place”? (1 mile = 1.61 kilometers)
32.17 square miles had to shelter in place.
83.39 square kilometers had to shelter in place.
©2012, TESCCC
04/25/13
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Geometry
HS Mathematics
Unit: 08 Lesson: 01
Perimeter, Circumference, and Area KEY
4. Shelly is sewing a quilt that will be made from material pieces in the shape of parallelograms
with consecutive sides of 12 cm and 18 cm and with base angles of 30 o and 150o. Each of the
parallelogram material pieces will be trimmed with gold braid. How many centimeters of gold
braid will be needed to trim each piece? How many square centimeters of material will be
needed for each piece? How many inches of gold braid and square inches of material will be
needed? If necessary, round answers to the nearest tenth. (1 inch = 2.54 centimeters)
Gold braid: 60 cm; Area of material: 108 cm2
Gold braid: 23.6 inches; Area of material: 16.7 in. 2
5.
The circular lid for a lead drum to hold nuclear waste has a diameter of 3.2 feet. The material
from which it is made weighs 6.5 pounds per square foot. How much does the circular lid to the drum
weigh? If necessary, round answers to the nearest hundredth.
The lid would be 8.04 square feet with a weight of 52.28 pounds.
6.
Annette is replacing the square window in her workroom. The window has diagonals of 42
inches. How many feet, to the nearest tenth, of trim will be needed for the frame? How many square
feet, to the nearest tenth, of glass will be needed for the window pane?
Trim for the frame: 118.8 in.  9.9 ft
Area of glass: 882 in2 = 6.1 ft2
7.
Flying Saucers Pizza charges $0.15 per square inch of pizza. If a pizza is measured by the
diameter, how much will Flying Saucers Pizza charge for a 7-inch, 10-inch, and 14-inch pizza,
rounded to the nearest cent? From your results, do you think this is how the price of pizza is
determined? Explain.
7-inch pizza, A = (7/2)2  38.48 square inches, which would cost $5.77
10-inch pizza, A = (10/2)2  78.54 square inches, which would cost $11.78
14-inch pizza, A = (14/2)2  153.94 square inches, which would cost $23.09
Answers may vary. Sample answers: This is probably not how it would be determined because
large pizzas would be too high to purchase. Pizza makers may round area to nearest whole
number before multiplying by $0.15 to simplify calculations. Others may have a computer
programs that would not round until the end of calculations.
8.
Norma wanted to downsize the furniture in her kitchen so she purchased a new circular table
4
5
similar to the original circular table but only
the original size. If the circumference of the original
table was 440 centimeters and the area it covered was 15,406 square centimeters, what would be the
circumference and area covered by the new circular table? Round to the nearest square centimeter.
Circumference of the new circular table  352 centimeters
Area of the new circular table  9,852 square centimeters
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04/25/13
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