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### Solid Figures

7th Grade Common Core Georgia Performance Standards:

TCV.7.G.6 (3) Solve real-world and mathematical problems involving volume of cubes and right prisms.

TCV.7.G.6 (2) Compute the surface area of right rectangular prisms and cubes in real-world and mathematical problems.

TCV.6.G.2 Find the volume of a right rectangular prism with fractional edge lengths. Discover and apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.TCV.6.G.4 (1) Represent three-dimensional figures using nets made up of rectangles and triangles.TCV.6.G.4 (2) Use nets to find the surface area of geometric figures in real-world and mathematical problems.

Gail Sherman 2013

Huh?

Pardon Me?

Volume- CRCT Formula Sheet gives the following formula for the volume of rectangular prisms:
V = area of base x h

- Area of the base is just lw or length x width
- h is the height, or how tall it is.

Volume of a Rectangular Prism

- 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

Your Turn

5 in.

- 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

Volume of a Triangular Prism

- What is the shape of the BIG B base?
- triangle

- Find the area of B.
- (5x10)/2 = 25

- What is the height?
- 4

- Final Answer?
- 4(5x10)/2 = 100 units³

5

4

10

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.

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

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

Add the Parts of the Triangular Prism

Triangle

Triangle

Rectangle

Rectangle

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

Use the net to name the parts of the pyramid.

6 ft

- Square
- Triangle
- Triangle
- Triangle
- Triangle

5 ft

5 ft

Write Formulas & Compute

- Square
- Triangle
- Triangle
- Triangle
- Triangle

25

15

15

15

15

85ft

lw =

½ bh=

½ bh=

½ bh=

½ bh=

5x5 =

½ (5x6)=

½ (5x6)=

½ (5x6)=

½ (5x6)=

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