1. Chapter 10 Measurement Section 10.5 Surface Area

2. The surface area of a three-dimensional solid is the area of each of its surfaces (faces) combined. This even includes the bottom in most cases. To find the surface area of shapes that are polyhedra you find the area of each face and add them together. Nets A net for a three dimensional solid (polyhedra) is a way of “unfolding” the solid to see each face as a flat shape. The nets for a cube and rectangle are given below. frontleftrightback bottom top 3 3 3 3 3 3 3 3 front top bottom back side Surface Area is the area of 6 squares of length 3 on each side. Area of a square is 3·3=9. The area of 6 squares is 6·9=54. 5 3 2 2 3 3 5 5 3 Surface Area 2 rectangles 3 by 5 2 rectangles 2 by 5 2 rectangles 2 by 3 Total =2·(3·5)=30 =2·(2·5)=20 =2·(2·3)=12 62

3. 4 6 3 3 66 The figure to the right shows the net for a isosceles triangular prism. 2 rectangles 3 by 6 = 2·(3·6)= 36 1 rectangle 3 by 4 = 1·(3·4) = 12 6 6 4 h 2 triangles b=4, h= 3 7 The figure to the right shows the net for a cylinder. 2 circles of radius 3=2·  ·3 2 =18  1 rectangle 7 by 6  =7·6  = 42  Total 60  3 Total

4. 4 2 4 4 4 2 4 4 2 4 1 This is the net for a rectangular pyramid. 1 rectangle 2 by 4= 2·4= 8 2 triangles b=4, h 1 = 2 triangles b=2, h 2 = Total The surface area for the “buildings” we were drawing in section 8.6 can be computed by drawing the six different views. It is normally assumed that each face of a cube is 1 square unit. The six views are shown below along with each ones area. Top Area =3 Right Area =3 Left Area =3 Bottom Area =3 Front Area =6 Back Area =6 Total Surface Area = 3 + 3 + 3 + 3 + 6 + 6 = 24