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

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.

What is a Right Prism?

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?

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

10

5

Your Turn

Find area of the base.

What is the height?

Final Answer?

4 in

. 5 in.

9 in

.

4 x 5 = 20

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 base. (5x10)/2 = 25

What is the height? 4

Final Answer? 4(5x10)/2 = 100 units³

5

410

Nets

Draw a net of a cube. How many faces?

6

Surface Area of a Cube Let’s name the faces of our cube.

Front Back Top Bottom Left RightIf 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.

4

2

7

How does your net compare?

☺ It’s ok to be different! ☺

Now find the surface area.

4

2

7

.

.

Surface Area of a Rectangular Prism

Front =Back = Top = Bottom = Right = Left = Total =

4

2

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

4

2

7

Nets

Draw a net of a triangular prism.

How many faces?

4in.

5 in.

2 in.

Parts of the Triangular Prism

TriangleTriangleRectangleRectangleRectangle

4in.

5 in.

2 in.

Add the Parts of the Triangular Prism

Triangle Triangle Rectangle Rectangle RectangleTotal =

4in.

5 in.

2 in.

½bh= ½(5x4) =10

½bh= ½(5x4) =10

lw=5x2 = 10

lw=5x2 = 10

lw=5x2 = 10

50 in

Pyramid Net

Draw a net for the square pyramid

5 ft5 ft

6 ft

Use the net to name the parts of the pyramid.

Square

Triangle

Triangle

Triangle

Triangle

5 ft5 ft

6 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)=

2515151515

85ft