AREA
3D FIGURES AND NETS
SURFACE AREA
VOLUME
VOCABULARY
100
What is the area of this polygon?
7.5 square feet
100
This is a net of a _______________.
triangular pyramid
100
What is the surface area of this prism?
90 square units
100
What is the volume of this 3D figure?
V = lwh
V = 12 x 2 x 3
V = 72 feet3
100
The number of square units that fit into a 2D shape.
AREA
200
What is the area of the polygon shown below?
a = bh
a = 17 x 4
a = 68 cm2
200
Describe the faces on a triangular prism. How many and what shape?
Triangular prisms have two triangular faces and three rectangular faces.
200
What is the surface area of the prism?
SA = 142 in2
Top: 3 x 5 = 15
Bottom: 3 x 5 = 15
Front: 5 x 7 = 35
Back: 5 x 7 = 35
Left: 3 x 7 = 21
Right: 3 x 7 = 21
200
Robert wants to fill a rectangular trash can with water for a science project. The trash can measures 8 inches long, 5 ¼ inches wide, and 31 ½ inches tall. How much water is needed to fill it?
V = l w h
8 x 5 ¼ x 31 ½ = 1,323 cubic inches
200
The number of cubic units (or unit cubes) that can fit inside of a three dimensional shape.
VOLUME
300
Mario wants to paint the front triangular portion of his roof white. In order to buy enough paint, he needs to know the area of that part. What is the area?
For a triangle,A = ½bh
On Mario’s roof, A = ½ x 25 x 17
A = 212.5 feet2
300
How many faces, edges, and vertices does a rectangular prism have?
A rectangular prism has:
6 faces
12 edges
8 vertices
300
Find the surface area of the net of the square pyramid.
SA = 132 in2
triangles = 1/2(6 x 8) = 24
24 x 4 = 96
square = 6 x 6 = 36
96 + 36 = 132
300
Mrs. Kazansky has a box that measures 5 inches long, 2 inches wide, and 3 inches high. She would like to use this box to hold dice for her math activities. Each one is a cube, with a length of 1 inch. How many dice can she hold in this box?
Each die is one inch on a side or one cubic inch.
V = l w h
V = 5 x 2 x 3 = 30 in3
So, 30 dice can fit in the box.300
The number of unit squares needed to cover a 3D figure is called...
SURFACE AREA
400
Nora has a table that is shaped like the polygon shown. What is the area of the tabletop? 
A = ½ (h)(b1+ b2)
A = ½ (12)(36 + 24)
A = 360 square inches
400
Which of the following nets will create a cube? Select all.
A and D
400
What is the surface area of the triangular prism shown?
Surface Area = 294 cm2
Triangle: ½(4 x 6) = 12
Back Triangle: ½(4 x 6) = 12
Left Rectangle: 15 x 7 = 105
Right Rectangle: 15 x 7 = 105
Bottom Rectangle: 15 x 4 = 60
400
The volume of a fish tank 1280 cubic inches. If the length is 16 inches and the width is 10 inches, what is the height?
height is 8 inches.
V= l w h
1280 = 16 x 10 x h
1280 = 160h
8 = h
400
Why is area measured in units2 and volume measured in units3?
Area is measured in square units because it is used for two-dimensional shapes which have a length and a width.
Volume is measured in cubic units because it is used for three dimensional shapes which have a length, width, and height.
500
Katrina wants to carpet her living room. Using the diagram of her living room, find the area that must be carpeted.
The total area is 272 ft2.
500
What 3D figure will this net fold into?
Triangular Prism
500
Lauren is building a box to hold her art supplies. She wants the box to be 8 inches long, 6 inches wide, and 9 inches high. She does not want a top for this box. How much wood will she use to create this box?
Wood needed: 300 in2
Bottom: 8 x 6 = 48
Front: 8 x 9 = 72
Back: 8 x 9 = 72
Left: 6 x 9 = 54
Right: 6 x 9 = 54
500
How much water can fit in fish tank that is 24 inches by 12 inches by 16 inches?
V = l w h
V = 24 x 12 x 16
V = 1728 cubic inches
500
What is the difference between a rectangular pyramid and a triangular prism?
A rectangular pyramid has one rectangular base and four triangular sides that meet at one vertex
A triangular prism has two identical parallel triangular bases connected by 3 rectangular faces.