Nets & 3D Shapes
A flat pattern that can be folded into a 3-dimensional figure
Nets
Find the surface area of a cube with side lengths of 2 cm.
24 cubic centimeters
To find the surface area of a pyramid, you add the area of the base to the sum of the areas of these.
What are the triangular faces?
What is the volume of a rectangular prism that is 2.5 feet long, 1.5 feet wide, and 4/3 feet high?
5 cubic feet
You are wrapping a gift box that is 5in x 7in x 5in. How much wrapping paper is needed?
What is 190 in²?
A 3-dimensional figure with a pair of parallel faces called bases that are congruent polygons.
Prisms
Find the total surface area of a rectangular prism with length 10 cm, width 5 cm, and height 3 cm.
190 square centimeters
A square pyramid has a base side of 6 cm and a slant height of 5 cm. What is the total surface area?
96 cubic centimeters
A shipping box measures 14 inches long, 9 inches wide, and 6 inches high.
14×9×6=756
756 cubic inches
A child’s toy chest holds 6 layers of blocks, and each layer has 15 blocks. How many blocks can it hold?
What is 90 blocks?
If you have a net with four squares connected across and one square on the top and bottom of the second square across, the shape is.....
a cube
Find the surface area of a triangular prism with triangular bases of base 3 cm, height 4 cm, side 5 cm, and prism length 10 cm.
132 square centimeters
A square pyramid–shaped tent has a square base that measures 10 feet on each side.
Each triangular face has a base of 10 feet and a height of 12 feet.
How much fabric is needed to cover the entire outside of the tent (including the base)?
Base area:
10×10=10010 × 10 = 10010×10=100 ft²
Area of one triangle:
12×10×12=60\frac{1}{2} × 10 × 12 = 6021×10×12=60 ft²
Four triangles:
60×4=24060 × 4 = 24060×4=240 ft²
Total surface area:
100+240=340100 + 240 = 340100+240=340 ft²
Answer: 340 square feet
A roof section is shaped like a triangular prism.
The triangular base has:
base = 10 meters
height = 6 meters
The length of the prism is 15 meters.
Area of triangular base:
12×10×6=30\frac{1}{2} × 10 × 6 = 3021×10×6=30
Volume of prism:
30×15=45030 × 15 = 45030×15=450
Answer: 450 cubic meters
A decorative planter is shaped like a square pyramid.
The base measures 6 feet by 6 feet, and the height is 10 feet.
How much soil is needed to fill the planter?
Base area:
6×6=366 × 6 = 366×6=36
Volume:
13×36×10\frac{1}{3} × 36 × 1031×36×10
13×360=120\frac{1}{3} × 360 = 12031×360=120
Answer: 120 cubic feet
If you make a triangular prism from paper, the bases are _________and the lateral faces are _________
triangles
triangles
The top of a skyscraper is shaped like a square pyramid. Each side of the base is 60 meters, and the height of each triangle is 20 meters. What is the lateral area of the pyramid?
2400 square meters
A small triangular pyramid trophy has a triangular base with a base of 8 cm and a height of 6 cm.
Each of the three side faces is a triangle with a base of 8 cm and a height of 9 cm.
What is the total surface area of the trophy?
Base area:
12×8×6=24\frac{1}{2} × 8 × 6 = 2421×8×6=24 cm²
One side triangle:
12×8×9=36\frac{1}{2} × 8 × 9 = 3621×8×9=36 cm²
Three side triangles:
36×3=10836 × 3 = 10836×3=108 cm²
Total surface area:
24+108=13224 + 108 = 13224+108=132 cm²
Answer: 132 square centimeters
A sand pile is shaped like a square pyramid.
The base measures 8 feet by 8 feet, and the height of the pyramid is 9 feet.
(Hint: Volume of a pyramid = ⅓ × base area × height)
Base area:
8×8=648 × 8 = 648×8=64
Volume of pyramid:
13×64×9\frac{1}{3} × 64 × 931×64×9
13×576=192\frac{1}{3} × 576 = 19231×576=192
Answer: 192 cubic feet
A school supply cabinet measures 9 feet tall, 4 feet wide, and 3 feet deep.
What is the volume of the cabinet?
9×4×3=108
Answer: 108 cubic feet
How many rectangles does it take to make 6 rectangular prisms?
36 rectangles
City Park is a right triangle with a base of 40 yards and a height of 25 yards. On a map the park has a base of40 in and a height of 25 in. What is the area of the triangle on the map?
500 inches
A gift box is shaped like a rectangular pyramid.
The base measures 12 inches by 8 inches.
There are:
Two triangular faces with base 12 inches and height 10 inches
Two triangular faces with base 8 inches and height 9 inches
What is the total surface area of the gift box?
Base area:
12×8=9612 × 8 = 9612×8=96 in²
Two large triangles:
12×12×10=60\frac{1}{2} × 12 × 10 = 6021×12×10=60
60×2=12060 × 2 = 12060×2=120 in²
Two small triangles:
12×8×9=36\frac{1}{2} × 8 × 9 = 3621×8×9=36
36×2=7236 × 2 = 7236×2=72 in²
Total surface area:
96+120+72=28896 + 120 + 72 = 28896+120+72=288 in²
Answer: 288 square inches
The volume of a triangular prism is 384 units³. If the area of its base is 32 units², what is the height of the prism?
What is 12 units
A toy chest is shaped like a rectangular prism.
It measures 18 inches long, 10 inches wide, and 12 inches high.
You want to paint the entire outside of the chest, including the top.
How many square inches will you need to paint?
Front & back:
18×12=21618 × 12 = 21618×12=216
216×2=432216 × 2 = 432216×2=432
Left & right:
10×12=12010 × 12 = 12010×12=120
120×2=240120 × 2 = 240120×2=240
Top & bottom:
18×10=18018 × 10 = 18018×10=180
180×2=360180 × 2 = 360180×2=360
Total surface area:
432+240+360=1,032432 + 240 + 360 = 1,032432+240+360=1,032
Answer: 1,032 square inches