Geometry: Chapter Questions
1. How is the formula for area of a parallelogram related to area of a rectangle?
2. How is the formula for area of a triangle related to area of a rectangle?
3. How do you find the area of irregular shapes?
4. How do you find the area of shaded regions?
5. How do you find the volume of a rectangular prism with fractional edge lengths?
6. How do you find the surface area of a 3-dimensional figure using its net?
7. How do you use coordinates to find the length of a side of a polygon?
Geometry: Chapter Problems
Rectangles & Parallelograms
Classwork
Find the area of each figure.
1.
2.
3.
3.
4.
6. Do the rectangle and parallelogram below have the same area? Explain why or why not.
N 2.5 in 2.5 in. 3 in.
9 in. 9 in.
7. The length of a rectangle is 14.5 in and the width is 3.2 in. What is its area?
8. How do you find the area of a rectangle?
9. How do you find the area of a parallelogram?
10. What is true of the base and height of a parallelogram?
11. What is the base of a parallelogram whose height is 6 cm and whose area is 144 cm2?
Homework
Find the area of each figure.
12.
13.
14.
15.
16.
17. Do the rectangle and parallelogram below have the same area? Explain why or why not.
N 4 cm. 6 cm. 4cm.
12 cm. 12 cm.
18. The length of a rectangle is 17 m and the width is 5.25 m. What is its area?
19. How do you find the width of a rectangle when given the length and total area?
20. How do you find the base of a parallelogram when given the height and total area?
21. What is true of the base and height of a parallelogram?
22. What is the base of a parallelogram whose height is 7 cm and whose area is 63 cm2?
Triangles & Trapezoids
Classwork
Find the area of each figure.
23.
24.
25.
26.
27.
28. The triangle below has an area of 4.76 sq. in. If the base is 3.4 in., let h be the height in inches. Explain how the equation 4.76 in2= 12(3.4 in.)(h) represents the situation. Solve the equation.[1]
29. Find the height of a triangle whose area is 40 in2 and whose base is 10 in.
30. Darnell and Donovan are both trying to calculate the area of an obtuse triangle. Examine their calculations below.
Darnell’s Work / Donovan’s Work
A=12×3 in. ×4 in.
A=6 in2 / A=12×12 in. ×4 in.
A=24 in2
Which student calculated the area correctly? Explain why the other student is not correct.[2]
Find the area of the polygons.
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32.
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Homework
Find the area of each figure.
33.
34.
35.
36.
37.
38. Find the height of a triangle whose area is 50 in2 and whose base is 5 in.
39. Find the base of a triangle whose area is 71.4 m2 and whose height is 8.4 m.
40. Russell calculated the area of the triangle below. His work is shown.
A=12×43 cm ×7 cm
A=150.5 cm2
Although Russell was told his work is correct, he had a hard time explaining why it is correct. Help Russell explain why is calculations are correct.[3]
Find the area of the polygons.
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41.
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Area of Irregular Figures
Classwork
Find the area of each figure.
43.
45.
46.
Homework
Find the area of each figure.
47.
48.
49.
50.
Area of Shaded Figures
Classwork Find the area of each shaded region.
51.
52.
53.
Homework Find the area of each shaded region.
54.
55.
56.
3 Dimensional Solids & Nets
Classwork
Name the figure.
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57.
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Give the number faces, edges, and vertices of each shape.
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60.
61.
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62. Triangular pyramid
63. cube
identify the 3-dimensional figure from its net.
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NJ Center for Teaching and Learning ~ 39 ~ www.njctl.org
67. Draw the net for a rectangular pyramid.
68. Draw the net for a soda can.
Homework
Name the figure.
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NJ Center for Teaching and Learning ~ 39 ~ www.njctl.org
Give the number faces, edges, and vertices of each shape.
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NJ Center for Teaching and Learning ~ 39 ~ www.njctl.org
74. square pyramid
75. rectangular prism
Identify the 3-dimensional figure from its net.
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NJ Center for Teaching and Learning ~ 39 ~ www.njctl.org
79. Draw the net for a 4x4 fence post.
80. Draw the net for a piece of apple pie.
Surface Area
Classwork
Find the surface area of the figures given their nets.
81.
82.
83.
84.
Draw the net to find the surface area of each figure.
85.
86.
87. Marley was wrapping a present for her brother’s birthday. The present is 12 inches long, 6 inches wide, and 6 inches tall. Label the net below to find the surface area of the present and determine at least how many square inches of wrapping paper she needs to use.
88. Joseph wants to paint the surface of a wooden pyramid he built. Use the net below to calculate how many square centimeters of paint Joseph will need to buy in order to paint his pyramid.
Homework
Find the surface area of the figures given their nets.
89.
90.
91.
92.
Draw the net to find the surface area of each figure.
93.
94.
95. A cookie company designed a new box for their chocolate chip cookies. Using the net below, find the surface area of the new box so the company knows how many square inches of cardboard are required for each package.
96. The net below represents a box created to ship clothing. The box below has a length of 7 in, a width of 5 in, and a height of 2 inches. Label the dimensions on the net below and find the total surface area of the box.
Volume
Classwork
Find the volume of each figure:
97. A 23 m x 16 m x 25 m rectangular prism
98. A cube with edge of 57 ft
99. A box has volume of 24 ft3 and a base of 2 ft by 3 ft, what is its height?
100.
101. The length, width and height of one of the small cubes is 13 m.
Find the volume of the figure.
102. The length, width and height of one of the small cubes is 35 cm.
Find the volume of the figure.
103. The length, width and height of one of the small cubes is 19 in.
Find the volume of the figure.
104. The length, width and height of one of the small cubes is 34 m.
Find the volume of the figure.
Homework
Find the volume of each figure:
105. A 45 m x 12 m x 78 m rectangular prism
106. A cube with edges of 49 ft
107. A box has volume of 24 ft3 and a base of 2 ft by 4ft, what is its height?
108.
109. The length, width and height of one of the small cubes is 23 m.
Find the volume of the figure.
110. The length, width and height of one of the small cubes is 14 ft.
Find the volume of the figure.
111. The length, width and height of one of the small cubes is 15 mm.
Find the volume of the figure.
112. The length, width and height of one of the small cubes is 18 m.
Find the volume of the figure.
Surface Area and Volume Application Problems
Classwork
113. A birthday gift is placed inside the box shown. Draw and label a net for this box, and show how you can use the net to determine the minimum amount of wrapping paper needed to wrap this gift?
114. The inside of a refrigerator in a medical laboratory measures 17 in by 18 3/4 in by 42 4/5 in. How much space is inside the refrigerator?
115. If a gallon of water is about 215 sq in, approximately how many gallons of water can fit inside this bathtub?
116. This wafer is going to be completely dipped in chocolate. How many square cm need to be covered?
Homework
117. Blake is donating some outgrown clothes to charity. How many cubic feet of clothes will fit in the box?
118. Blake must wrap the box in packaging paper. Draw and label a net for this box, and show how you can use the net to determine the minimum amount of packaging paper needed to wrap this box?
119. The Johnson family wants to paint their living room. This is a diagram of the room. If one gallon of paint will cover 32 square feet, how many gallons will they need in order to paint their room?
120. A candy company is designing the packaging for its new candy bar. The bars will be packed in cartons which are 1 foot long, 1 foot wide, and 1 foot high. How many of these cartons can they pack into the shipping crate which is 5 ft long, 12 ft wide, and 4 ft high?
Polygons in the Coordinate Plane
Classwork
121. Plot the following points and connect them in the order given. Find the distance of each side.
A (2.5,2)
B (-5 ½ 2)
C (-5 ½, 5)
D (2.5,5)
122. Plot the following points and connect them in the order given. What would be the coordinate of a fourth point that would form a parallelogram?
R (4,-1)
S (-1,-1)
T (-4,-4)
123. Without plotting the points, find the perimeter of the shape given its coordinates.
A (4,-4) B (1,-4) C (1,-1) D (4,-1)
124. Without plotting the points, find the area of the shape given its coordinates.
H (-2,-5) I (-2,-2) J (4,-2) K (4,-5)
125. Plot the following points in the order given. What is the name and the area of the shape formed?
D (-2,5)
E (-5,0.5)
F (5,0)
G (2,5)
126. Plot the following points in the order given. What is the area of the shape formed?
P (-3,1)
Q (-5,-4)
R (-1,-4)
Use the following map to answer the questions below.
127. The town library forms a square with Sebastian’s house, Ulysses’ house and Rodger’s house. What is the location of the town library? Plot and label it on the map.
128. What is the area of the square those locations form?
129. The grocery store forms a parallelogram with Tara’s house, Quincy’s house, and Sebastian’s house. What is the location of the grocery store? Plot and label it on the map.
130. What polygon does Sebastian’s house, Quincy’s house and the town library form? Be as specific as possible. The, give the area that this shape covers.
131. The schoolhouse is in the third quadrant, and forms a right, scalene triangle with Ulysses’ house and the grocery store. What is the location of the schoolhouse? Plot and label it on the map.
132. What is the area of that triangle?
133. The town library, the grocery store and the schoolhouse form a trapezoid with which location?
Homework
134. Plot the following points and connect them in the order given. Find the distance of each side.
A (2,2.5)
B (-3,2½)
C (-3,-2)
D (2,-2)
135. Plot the following points and connect them in the order given. What would be the coordinate of a fourth point that would form a parallelogram?
R (2,-2)
S (-2,-2)
T (0,-5)
136. Without plotting the points, find the perimeter of the shape given its coordinates.
A (2,-1) B (5,-1) C (5,-5) D (2,-5)
137. Without plotting the points, find the area of the shape given its coordinates.
H (1,5) I (1,1) J (-5,1) K (-5,5)
138. Plot the following points in the order given. What is the area of the shape formed?
D (1,1)
E (4,5)
F (-2,5)
G (-5,1)
139. Plot the following points in the order given. What is the name and the area of the shape formed?
P (-2.5,3)
Q (-2,-2)
R (4 ½ -2)
Use the following map to answer the questions below.
140. Flemington forms a trapezoid with Cutler, Dixon and Brookdale. What is the location of the town Flemington? Plot and label it on the map.
141. Brookdale, Dixon and Flemington, and Rockaway form a square. What is the location of the Rockaway? Plot and label it on the map.