Squares and Cubes
36 square meters is a perfect square.
What are the side lengths of this square?
Side lengths are 6 meters
A rectangular prism has dimensions...
Height = 2 cm
Width = 2 cm
Length = 5 cm
How many square units make up the surface area?
Front = 5 x 2 = 10 square cm --> back = 10 cm2
Right = 2 x 2 = 4 square cm --> left = 4 cm2
Top = 5 x 2 = 10 square cm --> bottom = 10 cm2
10 + 10 + 4 + 4 + 10 + 10 = 48 square cm
Top
What is the name of a polyhedron that has equivalent faces on the base and on the opposite face?
Prism
Find the area of a parallelogram with a base of 5 inches and height of 4 inches.
HINT: Record your answer in square inches for credit!
20 square inches
20 inches2
If a cube has a height of 5 inches, what is its volume?
HINT: Record your answer in cubic inches
5 * 5 * 5 = 125 cubic inches or 125 inches3
How can two figures have the same volume but different surface areas?
They could be rearranged to put more square units on the surface instead of concealed inside.
What is the specific name of a polyhedron that has a base face of a pentagon and a vertex on the opposite side?
Pentagonal pyramid
What three things does a height need to have to match with a base?
HINT: You need all 3 to earn credit
*At a right angle to the base
*Travel from the base
*Goes to the farthest point
If a cube has an edge with length 5 inches, what is the surface area of the cube?
Hint: All faces on a cube are the same type of polygon. Find one and you'll find them ___________.
Front = 5 * 5 = 25 square inches
25 square inches * 6 faces = 150 square inches
Mr. Nee will draw you the net of a triangular prism. Find the surface area of this triangular prism.
Base = 3 * 4 / 2 = 6 square inches
Rectangle 1 = 6 * 4 = 24 square inches
Rectangle 2 = 5 * 6 = 30 square inches
Rectangle 3 = 3 * 6 = 18 square inches
Base + Opposite + Rectangle 1 + R2 + R3
6 + 6 + 24 + 30 + 18 = 84 square inches
1.) The corners where the lines meet
2.) Where one line is shared by two faces
3.) The three dimensions we measure on the shape
1.) Vertex
2.) Edge
3.) Length, width, and height
What is the area of a triangle with a base of 4 cm and a height of 8 cm?
HINT: Finding the area of triangles is different than finding the area of a parallelogram.
A = b * h / 2
A = 4 * 8 / 2
A = 32 / 2
A = 4 square cm or 4 cm2
What is the largest cube that could be made (out of whole cubes) if I gave you 130 cubic units to use?
The cube would have:
Length = 5 units
Width = 5 units
Height = 5 units
The volume would be 125 cubic units
A rectangular pyramid has a base of 50 feet and a height of 100 feet. What is the surface area of the pyramid?
Rectangle has 4 sides --> 4 triangular faces
Rectangle = 50 * 50 = 2,500 square feet
Triangles are identical = 50 ft * 100 ft / 2
= 5,000 / 2
= 2,500 square feet each
2,500 + 2,500 + 2,500 + 2,500 + 2,500 or 2,500 * 5
= 12,500 square feet
What is the difference between the volume and the surface area of a polyhedron?
Volume = the space inside of a figure
Surface area = the total area of all the faces on a figure
What strategy could you use to find the area of an irregular polygon?
Decompose and find their areas