1. 7th Grade Georgia Standard of Excellence:
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 three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Gail Sherman 2013

2. 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.

3. V = (Area of base) x (Height)
Volume
GMAS Formula Sheet gives the following formula for the volume of right prisms:
V = (Area of base) x (Height)
Area of the base is just lw or length x width
The height is how tall it is.
Huh?
What?
Pardon Me?

4. Volume of a Rectangular Prism (Review from 6th grade)
What is the shape of the base?
rectangle
Find area of the base.
3x10 = 30
What is the height? 5
Final Answer?
3x10x5 = 150 units³ 3 5 10

5. Your Turn 4 x 5 = 20 9 (l x w) x h= (4x5) x 9 = 180in
Find area of the base.
What is the height?
Final Answer?
4 in.
4 x 5 = 20
9 in. 9
(l x w) x h= (4x5) x 9 = 180in

6. Volume of a Triangular Prism
What is the shape of the BIG B base?
triangle
Find the area of base.
(5x10)/2 = 25
What is the height? 4
Final Answer?
4(5x10)/2 = 100 units³ 5 4 10

7. Nets
Draw a net of a cube.
How many faces? 6

8. Surface Area of a Cube Let’s name the faces of our cube. Front Back
Top
Bottom
Left
Right
If each side is 3 inches long, find the surface area.

9. 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

10. Rectangular Prism Just a box. Draw a net for this rectangular prism. 24 2 7

11. How does your net compare?
☺ It’s ok to be different! ☺
Now find the surface area. 4 2 7

12. Surface Area of a Rectangular Prism.
Surface Area of a Rectangular Prism . 4 2 7
Front =
Back =
Top =
Bottom =
Right =
Left =
Total =

13. Rectangular Prism Front = 4x7=28 Back = 4x7=28 Top = 2x7=14
Bottom = 2x7=14
Right = 2x4=8
Left = 2x4=8
Total = 100 units ²

14. Nets Draw a net of a triangular prism. How many faces? 4in. 2 in.

15. Parts of the Triangular Prism
Triangle Rectangle
4in.
2 in.
5 in.

16. Add the Parts of the Triangular Prism
Triangle Rectangle Total =
4in.
½bh= ½(5x4) =10
½bh= ½(5x4) =10
2 in.
lw=5x2 = 10
lw=5x2 = 10
5 in.
lw=5x2 = 10
50 in

17. Pyramid Net
6 ft
Draw a net for the square pyramid
5 ft
5 ft

18. Use the net to name the parts of the pyramid.
Square
Triangle
5 ft
5 ft

19. Write Formulas & Compute
lw =
½ bh=
5x5 =
½ (5x6)= 25 15
85ft
Square
Triangle