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? Edges? Vertices? 6 12 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 SA= (lw + lw) + (hl + hl) + (hw + hw) l=8 w=3 h=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 + 24 Surface Area = 136 cm 2
Pyramid What 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*h s = 2 b=2 h=3 4 Triangles 1 Square