3D Figures

 What is a 3D figure?  A solid shape with length, width, and height rectangular prisms cube cone cylinder pyramid

3D Figures

 Most 3D figures have  Faces – the flat surfaces or sides  Edges – where the faces meet each other  Vertices – points where the edges meet or the “corners”

3D Figures

 Let’s look at a cube. How many…..

 Faces?

6

 Edges?

12

 Vertices?

8

Surface Area

 Surface area – the total area of the OUTSIDE of an object  Example – Think of how much wrapping paper you would need to wrap a box.

 How do I find surface area?

 find the area of all the faces and add them together

Nets

 What is a net?  A net is the pattern made when a 3D figure is laid out flat showing each face of the figure. A net is folded to make a 3D figure.

Nets and Surface Area

 You can use nets to help you find the surface area of a 3D figure.

 If you take the net of a cube, you see all the faces are squares. You can find the area of 1 of the faces and multiply it by 6 to find the surface area of the entire cube.  Area of a square?

s  Cube:

SA=s*s*6 or s²*6

 s=3

Rectangular Prism

 Find the area of each face and add them all together. All of the faces are rectangles. How many faces?

 Top and bottom faces are the same, the front and back faces are the same, and the left and right faces are the same  l=8  w=3  h=4 SA= (lw + lw) + (hl + hl) + (hw + hw) SA = (8 x 3 + 8 x 3) + (4 x 8 +4 x 8) + (4 x 3 + 4 x 3) SA = ( 24 + 24 ) + ( 32 + 32 ) + ( 12 + 12) SA = 48 + 64 + 24 Surface Area =

136 cm 2

Pyramid

 What shapes make up the faces of a pyramid?

4 Triangles 1 Square  Find the area of the base and the area of the 4 sides. Add them together.

 Base Area= s*s  Side Area= (1/2)b*h  s = 2  b=2  h=3