2D Geometry: Chapter Questions
1.
What are some of the special relationships between angles?
2.
What are perimeter and circumference and how are they relevant in daily life?
3.
How is the formula for area of a parallelogram related to area of a rectangle?
4.
How is the formula for area of a triangle related to area of a rectangle?
5.
How do you find the area of irregular shapes?
6.
How do you find the area of shaded regions?
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2D Geometry: Chapter Problems
Determining if a Triangle is Possible
Classwork
1. Determine if triangles can be formed with the following side lengths:
a. 4 m, 12 m, 15 m
b. 8 yd, 5 yd, 13 yd
c. 7 in, 15 in, 23 in
d. 24 ft, 35 ft, 58 ft
e. 18 cm, 27 cm, 46 cm
2. Which of the following sets of angles could form a triangle?
a. 45°, 57°, 78°
b. 90°, 54°, 26°
c. 104°, 90°, 34°
d. 55°, 91°, 105°
e. 56°, 45°, 79°
3. Predict the length of the third side of a triangle whose known sides are lengths:
a. 5 in, 23 in
b. 7 m, 32 m
c. 8 in, 12 in
d. 12 cm, 15 cm
e. 43 yd, 57 yd
Homework
4. Determine if triangles can be formed with the following side lengths:
a. 7 m, 11 m, 17 m
b. 13 yd, 9 yd, 23 yd
c. 13 in, 23 in, 36 in
d. 5 ft, 23 ft, 29 ft
e. 27 cm, 35 cm, 46 cm
5. Which of the following sets of angles could form a triangle?
a. 52°, 37°, 95°
b. 107°, 39°, 34°
c. 112°, 90°, 68°
d. 52°, 94°, 108°
e. 48°, 53°, 79°
6. Predict the length of the third side of a triangle whose known sides are lengths:
a. 8 in, 37 in
b. 17 m, 26 m
c. 12 in, 25 in
d. 9 cm, 18 cm
e. 82 yd, 99 yd
Special Pairs of Angles
Classwork
7. If two angles have the same measure are they congruent?
8. Angle 1 and Angle 2 are complementary. If ∠1 has a measure of 420 what would the measure of ∠2
be?
9. Determine the measure of the unknown angle A in the figure below.
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10.
11.
12.
13.
What is the complement of 720?
If Angle 1 measures 480 and Angle 2 measures 420 are these angles complementary?
Angle R and S are supplementary. If Angle R measures 1150 what is the measure of Angle S?
What is the measure of Angle A?
14.
15.
16.
17.
What is the supplement of 720?
If Angle X measures 530 and Angle Y measures 1270 are these angles supplementary?
What is the complement of 680? Supplement?
Using what you know about vertical angles, find the measure of the missing angles. You must be
able to explain why.
Angle
Measurement
Reason
∠𝐴
65°
Given
∠𝐵
∠𝐶
∠𝐷
18. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 37o determine the
measures of the remaining angles. You must be able to explain why.
Angle
Measurement
Reason
∠1
∠2
∠3
∠4
∠6
∠7
∠8
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Homework
19. Angle M has a measure of 360 and Angle N has a measure of 240. Are these two angles congruent?
20. Angle r and Angle s are complementary. If ∠𝑠 has a measure of 260 what would be the measure of
∠𝑟?
21. Determine the measure of the unknown angle A in the figure below.
22.
23.
24.
25.
What is the complement of 90?
If Angle x measures 530 and Angle y measures 1270 are these angles complimentary?
Angle A and B are supplementary. If ∠𝐴 measures 970 what is the measure of ∠𝐵?
What is 𝑚∠𝐴?
26.
27.
28.
29.
What is the supplement of 90?
If 𝑚∠1 =480 and 𝑚∠2 = 420 are these angles supplementary?
What is the complement of 840? Supplement?
Using what you know about vertical angles, find the measure of the missing angles. You must be
able to explain why.
30. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 680 determine the
measures of the remaining angles. You must be able to explain why.
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Perimeter and Circumference
Classwork
Find the perimeter of each figure.
31.
32.
33.
34.
35. Determine the circumference of a circle with radius 5 cm.
36. Determine the circumference of a circle with radius 2.3 m.
37. Determine the circumference of a circle whose diameter is 8 m.
38. Determine the circumference of a circle whose diameter is 24.6 cm.
39. What is the diameter of a circle whose circumference is 47.1 m?
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Homework
Find the perimeter of each figure.
40.
41.
42.
43.
44. Determine the circumference of a circle whose radius is 3.5 m.
45. Determine the circumference of a circle whose radius is 32 inches.
46. Determine the circumference of a circle whose diameter is 32 inches.
47. Determine the circumference of a circle with diameter 8 feet.
48. What is the radius of a circle whose circumference is 13.188 cm?
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Rectangles & Parallelograms
Classwork
Find the area of each figure.
49.
50.
51.
52.
53.
54. The length of a rectangle is 10 in and the width is 3 in. What is its area?
55. How do you find the area of a rectangle?
56. How do you find the area of a parallelogram?
57. What is true of the base and height of a parallelogram?
58. What is the base of a parallelogram whose height is 4 cm and whose area is 44 cm 2?
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Homework
Find the area of each figure.
59.
60.
61.
62.
63.
64. The length of a rectangle is 17 m and the width is 6 m. What is its area?
65. How do you find the area of a rectangle?
66. How do you find the area of a parallelogram?
67. What is true of the base and height of a parallelogram?
68. What is the base of a parallelogram whose height is 7 cm and whose area is 63 cm 2?
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Triangles & Trapezoids
Classwork
Find the area of each figure.
69.
70.
71.
72.
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73.
74. Find the height of a triangle whose area is 20 in2 and whose base is 8 in.
Homework
Find the area of each figure.
75.
76.
77.
78.
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79.
80. Find the height of a triangle whose area is 25 in2 and whose base is 5 in.
Circles
Classwork
Find the area of each figure.
81.
82.
83.
84.
85.
86.
A goat is tied to a 5 m rope. What is the area of the grass he can eat?
What is the area of a circle with a radius of 7 cm?
What is the area of a circle with a diameter of 16 yd?
How do you find area of a circle when given radius?
Homework
Find the area of each figure.
87.
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88.
89.
90.
91.
92.
A circular sprinkler has a radius of 4 m. How much grass can the sprinkler water?
What is the area of a circle with a radius of 5 in?
What is the area of a circle with a diameter of 14 m?
How do you find area of a circle when given diameter?
Irregular Figures
Classwork
Find the area of each figure.
93.
94.
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95.
96.
Homework
Find the area of each figure.
97.
98.
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99.
100.
Shaded Figures
Classwork
Find the area of each shaded region..
101.
102.
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103.
Homework
Find the area of each shaded region.
104.
105.
106.
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2 Dimensional Geometry – Unit Review
Multiple Choice– Choose the correct answer for each question. No partial credit will be given.
1. Determine which set of sides cannot be used to form a triangle.
a. 8 in, 9 in, 15 in
b. 15 m, 27 m, 41 m
c. 9 yd, 9 yd, 17 yd
d. 4 ft, 9 ft, 13 ft
2. If an angle measures 90, what is the measure of its vertical angle?
a. 90
b. 180
140
c. 270
d. 360
x
3. ABC measures 62. Its complementary angle measures:
a. 28
b. 62
c. 208
d. 298
4. How can this angle be classified?
a. Acute
b. Right
c. Obtuse
d. Straight
5. What is the perimeter of an equilateral triangle with 6-inch sides?
a. 18 inches
b. 24 inches
c. 27 inches
d. 36 inches
6. A soccer field has a length of 100 yards and a width of 60 yards. What is the perimeter of the field?
a. 160 yards
b. 220 yards
c. 320 yards
d. 6000 square yards
7. What is the area of a rectangle with length 36 cm and width 4 cm?
a. 72 cm
b. 144 cm
c. 144 cm2
d. 72 cm2
8. What is the area of the figure pictured to the right?
a. 6 square units
b. 10 square units
c. 12 square units
d. 50 square units
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9. A triangle has an area of 36 yd2 and a base of 3 yd, what is the height of the triangle?
a. 12 yd
b. 24 yd
c. 108 yd
d. 324 yd
10. Find the area of the figure to the right.
a. 17 cm2
b. 20 cm2
c. 27 cm2
d. 36 cm2
11. Find the height of the parallelogram with a length of 50 in and an area of 275 in 2.
a. 5.5 in
b. 22 in
c. 5.5 in2
d. 11 in
12. Jewell wants to tile her kitchen floor with tiles that are 1.5 ft2. If her kitchen is 18 ft by 12 ft, how many
tiles will she need?
a. 40
b. 144
c. 216
d. 324
13. Find the area of the figure to the right.
a. 44 cm
b. 44 cm2
c. 54 cm2
d. 32 cm2
14. Find the area of the shaded region to the right.
a. 20 cm2
b. 40 cm2
c. 80 cm2
d. 120 cm2
15. Find the length of the base of a triangle with an area of 20 cm 2 and a height of 5 cm.
a. 4 cm
b. 8 cm
c. 15 cm
d. 100 cm
Short Constructed Response – Write the correct answer for each question.
16. A circular carpet covers an area of 201 cm 2. What is the radius of the carpet?
17. What is the diameter of a circle whose area is 38.04 in2?
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_________
d = __________
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18. In order to decorate for a party, you need to cover 3 rectangular tables with tablecloth. The tables
measure 36 in by 72 in. If you want 2 inches overhang on each side, how many square inches of
fabric would it take to cover the 3 tables?
__________
19. The doors in your home need to be painted. Each door measures 8 ft x 3 ft. You are amazed that you
have 22 doors to paint! A can of paint can cover 400 square feet. How many cans of paint will you
need to purchase?
__________
20. A diagram of the side of your shed is below. How much siding is needed to cover both sides of the
shed that are shaped as pictured?
__________
Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.
21. Your parents have offered to pay you to wallpaper the kitchen walls. The wallpaper that you want
costs $12/square foot. The rectangular kitchen measures 16 ft x 12 ft, with a height of 8 ft. One
doorway measures 8 ft x 3 ft and two windows measures 3 ft x 5 ft.
a. Calculate the area of the kitchen walls, pretending there are no windows or doorways .
b. What is the area of the kitchen walls, when the doorways and windows are taken into
account?
c. What will be the minimum cost to wallpaper the kitchen?
22. You have been asked to design a flower garden with an area of 52 ft2. The client has no
preference for the shape of the garden. It’s all up to you!
a. If it will cost $3/ft to put flowers in the garden, determine the total cost.
b. Provide two possible dimensions of the flower garden.
c. Identify the shape that has the smallest perimeter.
23. A decorator wants to install two picture windows, measuring 12 ft. x 8 ft. The windows will be
placed on a wall measuring 72 ft x 12 ft.
a. What is the area of the wall, without windows?
b. How much area will two windows cover?
c. Wallpaper, costing $6/square foot, will be purchased to cover the wall, once the windows
are installed. What will be the least amount of money spent on the wallpaper?
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24. A bag of grass seed can cover 120 square feet. Ms. Peabody wants to seed her front and back
yard. The front yard is rectangular in shape, measuring 10 ft x 8 ft. Her back yard has an irregular
shape and is pictured below.
A. Calculate the square footage of Ms. Peabody’s front yard.
B. Calculate the square footage of Ms. Peabody’s back yard.
C. How many bags of grass seed will Ms. Peabody need to purchase?
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Answer Key
1.
a.
b.
c.
d.
e.
Yes
No
No
Yes
No
a.
b.
c.
d.
e.
Yes
No
No
No
Yes
a.
b.
c.
d.
e.
18 in < Third Side < 28 in
25 m < Third Side < 39 m
4 in < Third Side < 20 in
3 cm < Third Side < 27 cm
14 yd < Third Side < 100 yd
a.
b.
c.
d.
e.
Yes
No
No
No
Yes
a.
b.
c.
d.
e.
No
Yes
No
No
Yes
a.
b.
c.
d.
18 in < Third Side < 45 in
9 m < Third Side < 43 m
13 in < Third Side < 37 in
9 cm < Third Side < 27 cm
e. 17 yd < Third Side < 181 yd
Yes
48°
27°
18°
Yes
65°
128°
108°
Yes
Complement = 22°, Supplement = 112°
Multiple answers for the reasons. Some
examples:
<b = 65° since it's vertical to a 65° angle and
vertical angles are congruent
<c = 115° since it's supplemental to <b and
to the 65° angle
<d = 115° since it's vertical to <c or
supplemental to <b
18. Multiple answers for the reasons. Some
examples:
<1 = 37° since it's an alternate exterior angle
to <5 and alternate exterior angles are
congruent
<2 = 143° since it's supplemental to <1
<3 = 37° since it's vertical to <5
<4 = 143° since it's supplemental to <3 and
<5 or since it corresponds to <2
<6 = 143° since it's vertical to <4 or since it's
an alternate interior angle to <2
<7 = 37° since it's vertical to <1 or since it's
an alternate interior angle to <3
<8=143° since it's vertical to <2 or an
alternate exterior angle to <4 or corresponds
to <6
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
2.
3.
4.
5.
6.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
No
64°
72°
81°
Yes
83°
70°
171°
No
Complement = 6°, Supplement = 96°
Multiple answers for the reasons. Some
examples:
<b = 40° since it's vertical to a 40° angle and
vertical angles are congruent
<c = 140° since it's supplemental to <b
<a = 140° since it's vertical to <c or
supplemental to the 40° angle
30. Multiple answers for the reasons. Some
examples:
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31.
32.
33.
34.
35.
36.
<1 = 68° since it's an alternate exterior angle
to <5
<2 = 112° since it's supplemental to <1
<3 = 68° since it's vertical to <5 or
corresponds to <1
<4 = 112° since it's supplemental to <3 and
<5
<6 = 112° since it's supplemental to <5 or
vertical to <4 or an alternate interior angle to
<2
<7 = 68° since it's vertical to <1 or an
alternate interior angle to <3
<8 = 112° since it's vertical to <2 or an
alternate exterior angle to <4
10 m
16 ft
16 in
24 m
31.4 cm
14.444m
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37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
25.12 m
77.244 cm
15 m
42 cm
100 m
18 ft
64 m
21.98 m
200.96 in
100.48 in
25.12 ft
2.1 cm
24 cm²
121 m²
84 in²
108 m²
80 cm²
30 in²
Area of a rectangle = length x width
Area of a parallelogram = base x height
The base and height always form a right
angle
11 cm
28 cm²
81 m²
50 in²
91 m²
143 cm²
102 m²
Area of a rectangle = length x width
Area of a parallelogram = base x height
The base and height always form a right
angle
9 cm
60 ft²
78 m²
30 in²
84 in²
195 m²
5 in
90 ft²
91 m²
56 in²
105 in²
135 m²
10 in
314 m²
379.94 in²
78.5 m²
153.86 cm²
200.96 yd²
Area of a circle = π x radius²
254.34 m²
254.34 in²
50.24 m²
78.5 in²
153.86 m²
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92. Divide the diameter by 2 to find the radius.
Then, area of a circle = π x radius²
93. 10,500 units²
94. 14,300 units²
95. 88 cm²
96. 85 mm²
97. 12,200 units²
98. 15,650 units²
99. 238.3125 in²
100.
58 ft²
101.
28.26 in²
102.
43 units²
103.
40 ft²
104.
42.14 cm²
105.
43 units²
106.
96 m²
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
D
A
A
C
A
C
C
A
B
C
A
B
B
A
B
8 in
6.96 in
9120 in2
2
240 ft2
A.. 448 ft2
B. 394 ft2
C. $4728
22. A. $156
B. Answers will vary
C. Answers will vary
23. A. 864 ft.
B. 192 ft.
C.$4,032
24. A. 80 ft2
B. 57.57 ft2
C. 2 bags
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