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Solid Figures
7th Grade Georgia Standard of Excellence:
MGSE7.G.6 Solve real-world and mathematical problems
involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals,
polygons, cubes, and right prisms.
Gail Sherman 2013
What is a Right Prism?
A right prism is a geometric solid that has a
polygon as its base and vertical sides
perpendicular to the base. The base and top
surface are the same shape and size. It is
called a “right” prism because the angles
between the base and sides are right angles.
Volume
 GMAS Formula Sheet gives
the following formula for
the volume of right prisms:
Pardon Me?
V = (Area of base) x
(Height)
 Area of the base is just lw
or length x width
 The height is how tall it is.
Volume of a Rectangular Prism
(Review from 6th grade)
 What is the shape of the base?
 rectangle
3
 Find area of the base.
 3x10 = 30
 What is the height?
 5
 Final Answer?
 3x10x5 = 150 units³
5
10
Your Turn
5 in.
 Find area of the base.
 What is the height?
9
 Final Answer?
(l x w) x h=
(4x5) x 9 = 180in
9 in.
4 x 5 = 20
Volume of a Triangular Prism
 What is the shape of the BIG B base?
5
 triangle
 Find the area of base.
 (5x10)/2 = 25
 What is the height?
 4
 Final Answer?
 4(5x10)/2 = 100 units³
4
10
Nets
 Draw a net of a cube.
 How many faces?
6
Surface Area of a Cube
 Let’s name the faces of our cube.






If
Front
Back
Top
Bottom
Left
Right
each side is 3 inches long, find the
surface area.
Add the areas of the 6 faces!







Front is…… 3x3=9
Back is……. 3x3=9
Top is……… 3x3=9
Bottom is… 3x3=9
Left is……… 3x3=9
Right is……. 3x3=9
And the TOTAL is 54 in²
Rectangular Prism
 Just a box.
 Draw a net for this rectangular prism.
2
4
7
How does your net compare?
2
4
7
☺ It’s ok to be different! ☺
Now find the surface area.
.
Surface Area of a Rectangular Prism
.
Front =
Back
=
Top
=
Bottom =
Right =
Left
=
Total =
2
4
7
Rectangular Prism







Front = 4x7=28
Back
= 4x7=28
Top
= 2x7=14
Bottom = 2x7=14
Right = 2x4=8
Left
= 2x4=8
Total = 100 units ²
2
4
7
Nets
 Draw a net of a triangular
prism.
 How many faces?
4in.
Parts of the
Triangular Prism
Triangle
Triangle
Rectangle
Rectangle
Rectangle
4in.
Add the Parts of the
Triangular Prism
Triangle
Triangle ½bh= ½(5x4) =10
Rectangle lw=5x2 = 10
Rectangle lw=5x2 = 10
Rectangle lw=5x2 = 10
Total = 50 in
½bh= ½(5x4) =10
4in.
Pyramid Net
6 ft
 Draw a net for the
square pyramid
5 ft
Use the net to name the parts
of the pyramid.
6 ft
 Square
 Triangle
 Triangle
 Triangle
 Triangle
5 ft
Write Formulas & Compute





Square
Triangle
Triangle
Triangle
Triangle
lw =
½ bh=
½ bh=
½ bh=
½ bh=
5x5 =
½ (5x6)=
½ (5x6)=
½ (5x6)=
½ (5x6)=
25
15
15
15
15
85ft