Area and Perimeter
Perimeter
Class Work
Find the perimeter of the following figures.
1.
2.
4.
5.
6.
7.
8.
9.
3.
The length of a rectangle is 7 cm and its width is 5 cm, what is the rectangles perimeter?
An equilateral triangle has sides of 8ft., what is the triangle’s perimeter?
A regular octagon has sides of 7in, find the perimeter.
The perimeter of a regular heptagon is 42 inches, what is the length of a side?
A rectangle has length 20 mm and perimeter 50 mm, what is the rectangles width?
The perimeter of a square is 18 inches; find the length of its diagonal.
Homework
Find the perimeter of the following figures.
10.
11.
12.
13. The length of a rectangle is 4 cm and its width is 2.5 cm, what is
the rectangles perimeter?
14. An equilateral triangle has sides of 12 ft., what is the triangle’s perimeter?
15. A regular nonagon has sides of 10in, find the perimeter.
16. The perimeter of a regular hexagon is 42 inches, what is the length of a side?
17. A rectangle has length 18 mm and perimeter 70 mm, what is the rectangles width?
18. The perimeter of a rectangle is 18 inches and has width 6in, find the length of its
diagonal.
Circumference
Class Work
19. What is the circumference of a circle with diameter 6in?
20. If the circumference of a circle is 20 cm, what is the radius of the circle?
21. If the circumference of a circle is 30𝜋 ft, what is the circles diameter?
22. Find the perimeter of the following:
23. How long is the spiral?
24. An arc is made from a circle with radius 6 cm has a central angle of 40o, what is the
length of the arc?
25. An arc is made from a circle with diameter 16 cm has a central angle of 140o, what is the
length of the arc?
26. The arc of a circle has length 12cm and a measure of 70o, what is the circle’s radius?
27. An arc of a circle is 60 m, if the circles diameter is 20m what is the arcs measure?
28. The inside lane of a track is 110 yds along its curved portion, if the chord that connects
the ends of the curve is 70 yds is the curve a semicircle? Justify your answer.
Homework
29. What is the circumference of a circle with diameter 8 in?
30. If the circumference of a circle is 50 cm, what is the radius of the circle?
31. If the circumference of a circle is 10𝜋 ft, what is the circles diameter?
32. Find the perimeter of the following:
33. How long is the spiral?
34. An arc is made from a circle with radius 16 cm has a central angle of 50o, what is the
length of the arc?
35. An arc is made from a circle with diameter 18 cm has a central angle of 120o, what is the
length of the arc?
36. The arc of a circle has length 8cm and a measure of 80o, what is the circle’s radius?
37. An arc of a circle is 100 m, if the circles diameter is 40m what is the arcs measure?
38. A football is punted 60 yds, if the height of the punt 40 yds does the ball path follow the
arc of a circle? Justify your answer.
Area of a Square
Class Work
39. Find the area of a square with sides 8 ft.
40. Find the area of a square with sides 6 in.
41. Find the area of a square with diagonals 5 cm.
42. Find the area of a square with perimeter 20 mm.
43. Find the length of a side square with area 49 m2.
44. Find the exact perimeter of a square with area 20 cm2.
Homework
45. Find the area of a square with sides 7 ft.
46. Find the area of a square with sides 16 in.
47. Find the area of a square with diagonals 12 cm.
48. Find the area of a square with perimeter 28 mm.
49. Find the length of a side square with area 64 m2.
50. Find the exact perimeter of a square with area 72 cm2.
Area of a Rectangle
Class Work
51. Find the area of a rectangle with sides 4 in and 8 in.
52. Find the area of a rectangle with sides 3 ft and 20 in.
53. Find the area of a rectangle with length 8 cm and diagonals 10 cm.
54. Find the area of a rectangle with width 6 cm and diagonals 8 cm.
55. If the diagonals of a rectangle are 12in and split the angles into 20o and 70o angles, what
is the rectangles area?
56. The area of a rectangle is 60 ft2 with width 8 ft, find the rectangles perimeter.
57. Cal is refinishing his kitchen that measures 8 ft 5 in by 12 ft 7 in. His contractor said that
he could save money by getting the tile himself. The one he likes is 10 in by 10 in @
$1.89 each and is sold in cases of 20 tiles. The contractor told Cal to get 10% extra for
cuts. How many cases should Cal get and what will it cost him?
Homework
58. Find the area of a rectangle with sides 6 in and 12 in.
59. Find the area of a rectangle with sides 4 ft and 18 in.
60. Find the area of a rectangle with length 5 cm and diagonals 13 cm.
61. Find the area of a rectangle with width 5 mm and diagonals 6 cm.
62. If the diagonals of a rectangle are 10 in splits the angles into 40o and 50o angles, what is
the rectangles area?
63. The area of a rectangle is 50 ft2 with width 4 ft, find the rectangles perimeter.
64. Cal is refinishing his bathroom that measures 6 ft 10 in by 10 ft 6 in. His contractor said
that he could save money by getting the tile himself. The one he likes is 8 in by 2 in @
$1.12 each and is sold in cases of 40 tiles. The contractor told Cal to get 10% extra for
cuts. How many cases should Cal get and what will it cost him?
Area of a Rectangular Region
Class Work
65. Find the area of the following regions.
A.
B.
66. A homeowner has a 30’ by 40’ house on a 200’ by 600’ lot. She wants to fertilize her
grass which covers the entire lot, except for where the house and the driveway, which is
20’ by 10’, occupy. If the company she hires charges $0.40 per sq yard per treatment
and her yard will require 3 treatments, how much will it cost her?
67. Geo built a 10’ wide patio around his 20’ by 30’ pool. What is the square footage of the
patio? Around the patio there is a 2’ wide flower bed, except for where the gate, which
4’ wide, is located. How much flower bed space is there? Around the flower bed is a
fence, including the gate, what is the total length of the fence? If the fence is 5’ and
requires to be stained each year. Brand X will cover in one coat and will cover 150 sq ft
fence, how many gallons does Geo need to buy?
Homework
68. Find the area of the following regions.
A.
B.
69. A homeowner has a 35’ by 40’ house on a 300’ by 500’ lot. She wants to fertilize her
grass which covers the entire lot, except for where the house and the driveway, which is
30’ by 15’, occupy. If the company she hires charges $0.50 per sq yard per treatment
and her yard will require 4 treatments, how much will it cost her?
70. Geo built a 15’ wide patio around his 25’ by 40’ pool. What is the square footage of the
patio? Around the patio there is a 3’ wide flower bed, except for where the gate, which
4’ wide, is located. How much flower bed space is there? Around the flower bed is a
fence, including the gate, what is the total length of the fence? If the fence is 6’ and
requires to be stained each year. Brand X will cover in one coat and will cover 200 sq ft
fence, how many gallons does Geo need to buy?
Area of an Irregular Region
Class Work
Find the approximate area of the region.
71.
Each square has sides of 3cm.
72.
Each square has sides of ½ mm.
Homework
Find the approximate area of the region.
73.
Each square has sides 2 in.
74.
Each square has sides 1/3 ft.
Area of a Triangle
Class Work
75. The base of a triangle is 10 in and height of 6 in, find the area of the triangle.
76. The hypotenuse of a right triangle is 13 cm and one leg is 5 cm, find the triangles area.
77. The hypotenuse of a right triangle is 12 mm. If one of the angles is 45o, find the area.
78. The hypotenuse of a right triangle is 9 mm. If one of the angles is 25o, find the area.
79. The area of a triangle is 80 cm2 with a base of 10 cm, what is the triangles height.
80. The area of a triangle is 60 in2, if the triangle is a 30-60-90, how long is the hypotenuse?
81. The base of a triangle is doubled and it height tripled, what is the effect on the area?
82. An acute triangle has sides 12, 10, and 13 in. If the altitude to the 10 in side is 12.5 in,
how long is the altitude to the 12 in side?
Homework
83. The base of a triangle is 8 in and height of 5 in, find the area of the triangle.
84. The hypotenuse of a right triangle is 17 cm and one leg is 8 cm, find the triangles area.
85. The hypotenuse of a right triangle is 10 mm. If one of the angles is 45o, find the area.
86. The hypotenuse of a right triangle is 11 mm. If one of the angles is 32o, find the area.
87. The area of a triangle is 120 cm2 with a base of 40 cm, what is the triangles height.
88. The area of a triangle is 70 in2, if the triangle is a 30-60-90, how long is the hypotenuse?
89. The base of a triangle is quadrupled and yet its area only tripled, how was the height
changed?
90. An acute triangle has sides 22, 24, and 25 in. If the altitude to the 25 in side is 23 in, how
long is the altitude to the 22 in side?
Area of a Parallelogram
Class Work
Find the area of the following parallelograms.
91.
92.
93.
94.
95.
96.
97.
98.
99. Vertices (1,3),
(4,6), (8,6), & (5,3)
Homework
Find the area of the following parallelograms.
100.
101.
102.
103.
104.
105.
106.
107.
108. Vertices (0,0),
(0,4), (5,7), & (5,3)
Area of Kites and Rhombi
Class Work
Find the area of the following figures.
109.
110.
111.
112. Find the shaded area.
113.
Find the shaded area
115.Vertices (0,0),(1,3)
(4,4), (3,1)
116. Vertices (2,2), (5,4)
(2,10), (-1.4)
Homework
Find the area of the following figures.
118.
119.
114.
117. Vertices (0,0)
(1,4),(9,9),(4,1)
120.
121. Find the shaded area.
122.
Find the shaded area
124. Vertices (2,0), (0,4)
(-2,0), (0,-4)
125. Vertices (7,1), (9,-1)
(11,1) (9, -6)
123.
126. Vertices (3,4)
(6,1), (3, -2), (0,1)
Area of a Trapezoid
Class Work
Find the area of the figure.
127.
128.
130.
131.
129.
Vertices (0,0), (8,0)
(1,3), (6,3)
132.Vertices (1,0)
(6,0), (3,6), (2,6)
133. A trapezoid with bases 16 in and 24 in has an area of 80 in2. Find the height.
134. A trapezoid with area 80 cm2 has a height of 8cm and a base 18cm. Find the second base.
135. An isosceles trapezoid has a base angle of 60o and legs of 8 mm. If the area of the
trapezoid is 40√3 mm2 find the length of both bases.
Homework
Find the area of the figure.
136.
137.
139.
140.
138.
Vertices (-4,0), (4,0)
(2,2), (-2,2)
141. Vertices (0,0)
(0,8),(3,9),(3,5)
142. A trapezoid with bases 25 in and 33 in has an area of 116 in2. Find the height.
143. A trapezoid with area 62 cm2 has a height of 11cm and a base 6cm. Find the second base.
144. An isosceles trapezoid has a base angle of 45o and legs of 10 mm. If the area of the
trapezoid is 100 mm2 find the length of both bases.
Area of a Regular Polygon
Class Work
Find the area of the regular polygon.
145. Pentagon with perimeter 54.5 mm and apothem 7.5 mm.
146. Square with apothem 4 in.
147. Hexagon with sides 6 ft.
148. Triangle with apothem 4cm.
149.
150.
151.
Octagon with radius 10 in.
Nonagon with perimeter of 18 cm.
A regular hexagon has area 36 in2, find the apothem.
Homework
Find the area of the regular polygon.
152. Pentagon with perimeter 60 mm and apothem 8.3mm.
153. Square with radius 4 in.
154. Hexagon with apothem 8 ft.
155. Triangle with radius 4cm.
156. Octagon with apothem 10 in.
157. Heptagon with perimeter of 28 cm.
158. A regular triangle has area 36 in2, find the apothem.
Area of a Circle
Class Work
159. The radius of a circle is 16 in, find the area.
160. The diameter of a circle is 24 cm, find the area.
161. The area of a circle is 36𝜋 ft2, find the radius.
162. The area of a circle is 49 cm2, find the circumference.
Find the area of the shaded region.
163.
164.
165.
Homework
166. The radius of a circle is 10 in, find the area.
167. The diameter of a circle is 11 cm, find the area.
168. The area of a circle is 16𝜋 ft2, find the radius.
169. The area of a circle is 81 cm2, find the circumference.
Find the area of the shaded region.
170.
171.
172.
Area of Sectors and Segments of a Circle
Class Work
Find the area of the sector.
173.
174.
175.
Find the area of the segment.
176.
177.
178.
Homework
Find the area of the sector.
179.
180.
181.
Find the area of the segment.
182.
183.
184.
Heron’s Formula
Class Work
185. Find the area of the triangle with sides 4, 6, and 8.
186. Find the area of the triangle with sides 6, 6, and 10.
187. Find the area of the triangle with sides 2, 4, and 6.
188. Find the area of the triangle with sides 5, 5, and 5.
Homework
189. Find the area of the triangle with sides 5, 7, and 8.
190. Find the area of the triangle with sides3, 5, and 7.
191. Find the area of the triangle with sides 10, 12, and 12.
192. Find the area of the triangle with sides 1, 2, and 4.
Brahmagupta’s Formula
Class Work
193. Find the area inscribable quadrilateral with sides 4, 5, 7, and 8.
194. Find the area inscribable quadrilateral with sides 5, 5, 6, and 8.
195. Find the area inscribable quadrilateral with sides 2, 10, 12, and 2.
Homework
196. Find the area inscribable quadrilateral with sides 3, 5, 6, and9.
197. Find the area inscribable quadrilateral with sides 4, 7, 8, and 8.
198. Find the area inscribable quadrilateral with sides 1, 2, 3, and 4.
Geometric Probability
Class Work
199. An elevator breaks down in a 30 story building, what is the probability it breaks down
between the 7th and 12th floors?
200. A car gets on the highway at mile post 17 and is suppose to exit at mile post 84. If the
car breaks down, what is the probability it breaks down within four miles of mile post 30?
201. Use the spinner to find the following:
a. P(A)
b. P(C)
c. P(A or B)
d. P(~D)
202.
Find the probability that a point inside the larger shape lies inside of the shaded region.
A
B.
C.
Homework
203. An elevator breaks down in a 20 story building, what is the probability it breaks down
between the 8th and 12th floors?
204. A car gets on the highway at mile post 20 and is suppose to exit at mile post 65. If the
car breaks down, what is the probability it breaks down within four miles of mile post 80?
205. Use the spinner to find the following:
e. P(A)
f. P(C)
g. P(A or B)
h. P(~D)
206.
1.
2.
3.
4.
5.
6.
Find the probability that a point inside the larger shape lies inside of the shaded region.
A
B.
C.
Multiple Choice
What is the difference in the perimeter of a hexagon with sides 6 and nonagon with sides 5?
a. 20
b. 11
c. 9
d. 1
A set of stairs consists of 9 treads and 10 risers. If the treads are 8 inches by 36 inches and
the risers are 7 inches by 36 inches, how many square feet of carpet would be needed to
cover the stairs?
a. 540
b. 568
c. 1704
d. 5112
A parallelogram has sides of 8ft and 10ft and an angle of 40o. Find the area of the
parallelogram.
a. 40 ft2
b. 51 ft2
c. 61 ft2
d. 80 ft2
The bases of a trapezoid are 6 cm and 12 cm and the height is 16 mm, find the area of the
trapezoid.
a. 288 cm2
b. 144 cm2
c. 14.4 cm2
d. 7.2 cm2
The vertices of a quadrilateral are (3,0), (5,3), (7,0), and (5,-4). Find the area of the figure.
a. 14 u2
b. 16 u2
c. 24u2
d. 28u2
The area of a sector of a circle is 7𝜋 in2. If the circle has a radius 4 in, find the measure of
the arc of the sector.
a. 112o
b. 140.2o
c. 157.5o
d. 166.3o
For questions 7 and 8, refer to the diagram at the right. All angles are right angles.
7. What is the area of the rectangular region shown?
a. 102 u2
b. 96 u2
c. 90 u2
d. 91 u2
8. What is the perimeter of the rectangular region shown?
a. 41 u
b. 50 u
c. 54 u
d. 66 u
9. What is the approximate area of the irregular region shown?
a. 243 u2
b. 211.5 u2
c. 81 u2
d. 70.5 u2
10. What is the area of a regular pentagon with a radius of 7 cm?
a. 116.5 cm2
b. 178 cm2
c. 233 cm2
d. 356 cm2
11. A triangle has sides 7, 8, and 13. Find the area.
a. 28 u2
b. 24.2 u2
c. 18.8 u
d. 6.5 u2
12. An inscribable quadrilateral has sides 4, 6, 8, and 8, find the area.
a. 17.7 u2
b. 39.7 u2
c. 143.1 u2
d. 377.6 u2
13. Using the spinner, find P(~ A)
a. 17/18
b. 11/18
c. 5/18
d. 1/18
14. A circle is inscribed in a square. Find the probability that a point randomly chosen inside of
the square is not inside the circle.
𝜋
a.
b.
c.
4
4−𝜋
4
𝜋−4
4
d. It will vary depending on the size of the square and circle.
Extended Response
1. Given the quadrilateral with vertices A(4,2), B(7,3), C(10,2), and D(7,1),
a. Explain what type of quadrilateral it is and show why.
b. Find the perimeter of the figure.
c. Find the area of the figure.
2. Circle B has radius 6 and ∠XBY has measure 40o.
a. Find the length of XY and arc 𝑋𝑌
b. Find the area of the sector XBY.
̅̅̅̅ .
c. Find the area of the segment cut off by 𝑋𝑌
3. A 3cm by 4cm rectangle is inscribed in a circle
a. Find the area of the rectangle.
b. Use Brahmagupta’s Formula to find the area. Show your work.
c. Divide the rectangle in a manner that Heron’s Formula can be used. Find the
area of the rectangle using Heron’s Formula. Show your work.
Answer
1. 48 u
2. (6+3√3) u
3. 108 u
4. 24 cm
5. 24 ft
6. 56 in
7. 6 in
8. 5mm
9. 4.5 2 in
10. 64 cm
11. (12+√74) u
12. 4 u
13. 13 cm
14. 36 ft
15. 90 in
16. 7 in
17. 17 mm
18. 3 5 in
19. 6π in
20. 10/ π cm
21. 30 ft
22. (21+1.5π) ft
23. 13.5 π u
24. (4/3) π cm
25. (56/3) π cm
26. (432/7π) cm
27. (1000/ π) degrees
28. no, because 110 doesn’t equal
(1/2)(70 π)
29. 8π in
30. (25/π) cm
31. 10 ft
32. (26π/9) +8 u
33. 19.5 π u
34. (40/9π) u
35. 6π u
36. (18/ π) cm
37. (900/ π) degrees
38. no, because 60 would be the
diameter so the radius would be 30
not 40
39. 64ft2
40. 36in2
41. 12.4cm2
42. 25 mm2
43. 7 in
44. 8√5 cm
45. 49 ft2
46. 256 in2
47. 72 cm2
48. 49 mm2
49. 8 m
50. 242 cm
51. 32 in2
52. 720 in2
53. 48 cm2
54. 12√7
55. 46.281 in2
56. 31 ft
57. 10 cases at $378
58. 72 in2
59. 864 in2
60. 60 cm2
61. 5√4 mm
62. 49.24 in2
63. 33 ft
64. depending on direction of tile: 20
cases at $896 or 19 cases at
$851.20
65. A) 198 u B) 44 u2
66. $10,480
67. Ratio: 1400 ft2 Flower bed: 384 ft2
Fence: 196 ft Stain: 14 gal (fence
has two sides)
68. A) 16 u2 B) 56 u2
69. $32,922.22
70. Patio: 2850 ft2 flower bed 540 ft2
Fence 274 ft Stain: 17 gal
71. approximately 481.5 cm2
72. approximately 21.75 mm2
73. approx. 464 in2
74. approx. 7.39 ft 2
75. 30 in2
76. 30 in2
77. 36 mm2
78. 15.5 mm2
79. 16 in
80. 16.65 in
81. 6 times
82. 10.416 in
83. 20 in
84. 60 cm2
85. 25 mm2
86. 27.19 mm2
87. 6 cm
88. 17.98
89. by ¾
90. 26.14 in
91. 12u2
92. 20mm2
93. 40ft2
94. 12…
95. 20mm2
96. 67.66 u2
97. 10√3
98. 31.5√3 m
99. 12 u2
100. 54 in2
101. 48 in2
102. 112 m2
103. 56 m2
104. 33 u2
105. 103.4 u2
106. 24.5 m2
107. 84√2
108. 20 u2
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
30 u2
48 u2
200 u2
30 u2
18 u2
49 u2
8 u2
24 u2
27 u2
16 u2
80 u2
98 u2
48 u2
144 u2
23.14 u2
16 u2
10 u2
18 u2
80 u2
34.5u2
180 u2
21.14 u2
19.5 u2
18 u2
4 in
2 cm
6mm +14 mm
50 u2
80 u2
80.5 u2
326.1 u2
12 u2
18 u2
4 in
5.27
5√2 + 15√2
204.375
64 in2
54√3 𝑓𝑡
48√3
149.
150.
151.
152.
153.
154.
155.
156.
157.
158.
159.
160.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
171.
172.
173.
174.
175.
176.
177.
178.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
282.84 in2
24.73 cm2
3.22 in
249 mm2
32 in2
221.70 ft2
12√3
2090.5in2
58.14 cm
2.63 in
256π in2
144 π cm2
6 ft
3.95 cm
18 π u2
36 π u2
32+6 π u2
100 π u2
27.5 π u2
4 ft
5.08 cm
32 π u2
64 π u2
10.5 π u2
2.79 u2
25. 13 u2
47.04 u2
.127 u2
14.27 u2
8.55 u2
1.57 u2
2.83 u2
113.45
.095 u2
19.57 u2
43.30 u2
11.6 u2
166 u2
triangle is not possible
10.83 u2
189. 17.3 u2
190. 6.5 u2
191. 54.5 u2
192. triangle is not possible
193. 33.47 u2
194. 34.29 u2
195. 19/05 u2
196. 27.56 u2
197. 43.22 u2
198. 4.9 u2
199. 1/6
200. 8/67
201. A) 1/18 B) ¼ C) ¼ D) ½
202. A) ½ B) (48 π-36√3) / (48 π) C)
4/9
203. 1/5
204. 0
205. A) 1/36 B) 7/36 C) ¼ D) 4/9
206. A) ½ B) (64π-96√3)/ (64π) C)
7/12
Multiple Choice
1. C
2. D
3. B
4. C
5. A
6. C
7. C
8. D
9. B
10. A
11. B
12. B
13. A
14. C
Extended Response
1. A. Rhombus, all sides = √10
B. 4√10 𝑢
C. 6 u2
2. A. length of arc XY= 4.19 u; XY= 4.10u
B. 11.57 u2
C. .996 u2
3. A. 12 cm2
B. s=7; 𝐴 = √3(4)(3)(4) = 12𝑢2
C. use a diagonal=5; s=6
Area of 1 triangle= √6(1)(2)(3) = 6𝑢2
Area of rectangle = area of 2 triangles=
12u2