Geometry
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Measurement of Two-Dimensional Figures PI
The Pentagon in Washington D.C., home to the Department of Defense, is one of the most
recognizable buildings to people living in the United States because of its unique five sided shape.
The Pentagon is actually an arrangement of five concentric pentagonal rings that form the buildings
which house offices. Assume that the Pentagon is a regular polygon, and each outer wall has a length
of 921 ft.
1.
Find the perimeter of the outer wall.
2.
Find the area, to the nearest square foot, contained within the perimeter of the outer wall of the
Pentagon.
3.
Calculate the perimeter in meters, rounded to the nearest meter and the area in square
meters, rounded to the nearest square meter. (3.28 feet ≈ 1 meter)
The concentric pentagonal rings that form the Pentagon are labeled from the interior outward as
Ring A, Ring B, Ring C, Ring D, and Ring E. In problem 1 you found the perimeter of the outside of
Ring E and the area contained inside the outer wall of Ring E. Suppose the length of the inside of the
2
5
inner most wall, that of Ring A, is
that of the outermost wall of the Pentagon.
4.
What is the perimeter of the innermost wall in
feet?
.
5.
What is the area contained inside the
innermost wall of the Pentagon or Ring A,
rounded to the nearest foot?
6.
What is the ratio of areas of the two pentagons? Explain the significance of the ratios of the
2
5
areas in terms of the scale factor .
©2012, TESCCC
04/26/13
page 1 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
©2012, TESCCC
04/26/13
page 2 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Measurement of Two-Dimensional Figures PI
Goat on a rope!
A
C
B
Your prized Nubian goat, Nelly, has managed to escape her pen
and has once again been caught grazing in your neighbor’s
pepper patch. Your neighbor is furious and demands that you tie
the goat immediately until the pen can be repaired. You comply
and decide to tether the goat to your barn using a 20 ft. rope. Your
barn is in the shape of a rectangle and has dimensions 30 ft. by
16 ft. Point B is the midpoint of the longer side and point C is the
midpoint of the shorter side.
7.
Create a diagram to show the grazing areas for Nelly if she is tethered from point A, point B,
and point C using a rope 20 ft. in length. Use your diagram to,
a. Calculate the grazing areas for Nelly from point A, point B, and Point C to the nearest
square foot.
b. Calculate the maximum distance Nelly would be able to walk if tethered from point A,
point B, and point C to the nearest foot.
c. Which of the tether points will allow Nelly the greatest amount of grazing area?
©2012, TESCCC
04/26/13
page 3 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Measurement of Two-Dimensional Figures PI
8.
Find the perimeter and the area of the shaded region of each figure. Round answers to the
nearest hundredth when necessary. Box answers.
12 cm
Regular hexagon with inscribed equilateral triangle
8m
2m
2m
a.
b.
10 m
20 m
48 m
12 cm
20 cm
36 cm
6 cm
16 cm
c.
©2012, TESCCC
d.
04/26/13
page 4 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Measurement of Two-Dimensional Figures PI
9.
Find the arc length and the area of each shaded region or sector of the circle. Round to the
nearest hundredth.
135o
8m
60o
12 cm
a.
b,
90o
6 ft
c.
10. The front side window of a car is in the shape of the trapezoid below. The factory has been
contracted to make 2,500 of the windows. What is the minimum number of square meters of
glass needed to complete the order? To the nearest hundredth, what is the minimum number
of square feet needed to complete the order? (3.28 feet = 1 meter)
40 cm
36 cm
48 cm
37 cm
©2012, TESCCC
04/26/13
page 5 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
©2012, TESCCC
04/26/13
page 6 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Measurement of Two-Dimensional Figures PI
11. Marsha is carpeting her living room/dining room combination. The plan below shows the
dimensions of the rooms. The carpet she has selected costs $19.95 per square yard.
Approximately how much, to the nearest cent, will it cost her to carpet the rooms?
15 feet
17 feet
8 feet
7 feet
28 feet
4.5 feet
12. Use a hexagon split in equal sections to represent a probability of 1/3.
13. If a dart must land in the circle, what is the probability of it landing in the triangular region?
20 m
48 m
©2012, TESCCC
04/26/13
page 7 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
©2012, TESCCC
04/26/13
page 8 of 9
Geometry
HS Mathematics
Unit: 08 Lesson: 01
Evaluating Measurement of Two-Dimensional Figures PI
3
5
14. The probability of winning a one person card game is . If two people play the game, what
are the following probabilities? Use an area model to determine the probability. Show all
work.
a. Both of them will win?
b. Only one of them will win and the other loses?
c. Neither of them will win?
©2012, TESCCC
04/26/13
page 9 of 9