Area of Parallelograms
What two measurements are needed to find the area of a parallelogram?
Base
Height
Before dividing by 2, what two measurements are needed to find the area of a triangle?
Base
Height
What quality makes a pyramid?
What is a good definition for surface area?
Surface area is the area on all the faces of a three-dimensional shape put together.
It is the sum of the area of all polygonal faces.
Is volume the same thing as surface area? Yes or no?
No! Volume is the amount of cubic space a polyhedron takes up.
What is the formula or rule for finding the area of a parallelogram?
Area = base ⋅ height
A = b ⋅ h
What is the formula or rule for finding the area of a triangle?
Area = base ⋅ height ÷ 2
What quality makes a prism?
It has a base face and opposite of it is an equal and identical face.
Mr. Nee --> open Net1.jpg in downloads
Do not calculate the area of this prism, but instead... can you find the surface area of this prism from its net? How do you know?
Yes, the opposite sides on all parallelograms are the same! If one is labelled, you know the other side.
How do you know if a base and height are a corresponding (or matching) pair?
Base and height are perpendicular (they meet at a right angle)
The height travels from the base to the opposite side or vertex
A triangle is a type of polygon. What qualities make up a polygon?
Two-dimensional (flat)
Closed
Straight lines
Mr. Nee will hold up a polyhedron.
To get the full name of the polyhedron, name the base and then decide if opposite is an identical face or a vertex.
Square pyramid
Mr. Nee --> open Net1.jpg in downloads
What is the surface area of this rectangular prism?
Remember: It has 6 total faces. Base (bottom) and top, front and back, and left and right.
Base = 9 ⋅ 4 = __________
Top = 9 ⋅ 4 = __________
Front = 4 ⋅3 = __________
Back = 4 ⋅ 3 = __________
Left = 9 ⋅ 3 = __________
Right = 9 ⋅ 3 = __________
Surface area = ___________ square meters
What is the volume of this rectangular prism?
Record your answer with cubic units
Volume = length x width x height
Volume = 3 x 2 x 13
V = 6 x 13
V = 78 cubic inches
Mr. Nee --> open Parallelogram2.png from downloads
What is the area of this parallelogram?
First, multiply the two factors you will need.
Then, your product will be your area.
Finally, make sure to label the units!
Area = 15 square units
15 units2
Mr. Nee --> open triangle.png from downloads
Find the area of this triangle.
First, find the correct base and height.
Then, use the correct formula to calculate.
Finally, record your answer with the correct unit!
15 square units
15 units2
Mr. Nee will hold up a polyhedron.
To get the full name of the polyhedron, name the base and then decide if opposite is an identical face or a vertex.
Rectangular prism
Mr. Nee --> open Cube.jpg
What is the surface area of this cube?
Remember: a cube has 6 faces and they are all the ___________!
If one face is a 2 x 2 square, its area is 4 square inches.
To solve for surface area of a cube, find one square, and multiply it by 6.
4 square inches x 6 faces = ______________
Mr. Nee --> Open Parallelogram.png in downloads
Find the area of this parallelogram.
First, show your work by writing the factors you have to multiply.
Then, your product is your answer.
Last, make sure to label with the correct unit!
20 square cm
20 square centimeters
20 cm2
First... what are the correct math names for these things:
Corners where lines meet
Lines where faces meet
Area of a flat shape on a polyhedron
Then... how many of each of these things is on a cube?
Corners = vertices; 8 on a cube
Lines = edges; 12 on a cube
Flat shapes = faces; 6 on a cube
Mr. Nee --> open pyramid.svg from home
What is the surface area of this pyramid?
Remember: Find the area of each face and put them together!
In a pyramid, all the triangular faces will be the ________!
Area of square = base x height
5 x 5 = 25 square cm
Area of triangle = base x height ÷ 2
5 x 8 ÷ 2
40 ÷ 2 = 20 square cm
4 triangles = 4 x 20 square cm = 80 square cm
80 square cm + 20 square cm =
100 square cm