3D Figures, Surface Area and Nets

3D FiguresWhat is a 3D figure?

A solid shape with length, width, and height

rectangular prisms cube

cone cylinder

pyramid

3D FiguresMost 3D figures have

Faces – the flat surfaces or sides Edges – where the faces meet each otherVertices – points where the edges meet or the

“corners”

3D FiguresLet’s look at a cube. How many…..

Faces?

Edges?

Vertices?

6

12

8

Surface AreaSurface 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

NetsWhat 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 AreaYou 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*6s=3

Rectangular PrismFind 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

SA= (lw + lw) + (hl + hl) + (hw + hw)

l=8w=3h=4

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 + 24Surface Area = 136 cm2

PyramidWhat shapes make up the faces of a pyramid?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*hs = 2b=2h=3

4 Triangles1 Square