3 D Figures Surface Area and Nets 3

3 D Figures, Surface Area and Nets

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

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

3 D Figures �Let’s look at a cube. How many…. . � Faces? � Edges? 6 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 3 D figure is laid out flat showing each face of the figure. A net is folded to make a 3 D figure.

Nets and Surface Area �You can use nets to help you find the surface area of a 3 D 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 = (8(lw x 3 ++8 lw) x 3) ++(4(hl x 8+ +4 hl) x 8) + + (4 x 3 ++4 hw) x 3) SA= (hw SA = ( 24 + 24 ) + ( 32 + 32 ) + ( 12 + 12) �l=8 SA = 48 + 64 + 24 2 Surface Area = 136 cm �w=3 �h=4

Pyramid 4 Triangles pyramid? 1 Square �What shapes make up the faces of a �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