Surface Area and Volume 2 Explore Surface Area Using Nets for Visual Learners Fortner

Base 6 x 4 Lateral Face 8 x 6 Lateral Face 8 x 4 Base 6 x 4 Lateral Face 8 x 4 Latera Face 6 x 8

208

Counting the grid squares on each face and then found the sum of the grid squares on all 6 faces. You could find the product of the Length and Width of each face.

6 cm 8 cm 6 cm 4 cm 4 cm 6 cm

length width 6 cm 8 cm 6 cm 4 cm 4 cm 6 cm

6 cm 8 cm 6 cm 4 cm 4 cm 6 cm 48 24 24 32 48

32 + 24 + 48 + 24 + 32 + 48 208

Finding the areas of the faces using the formula for the area of a rectangle is an equivalent but faster method of finding the areas by counting grid squares.

Two faces have areas of 48 cm², two have areas of 32 cm² and two have areas of 24 cm². Find the surface area by doubling 48, 32, and 24 and finding their sum.

Find the area of one face and then multiply it by 6.

2 x 4 2 x 3 4 x 3 2 x 3 4 x 3 2 x 4 6 8 12 6 8 12 8 + 6 + 12 + 6 + 12 + 8 52

5 x 5 25 25 x 6 150

222 Lateral Face 9 x 3 Base 7 x 3 Lateral Face 9 x 3

100 A 10 x 10 100 x 6 600

Lateral Face 15 x 5 15 x 5= 75 Base 5 x 5 15 x 5= 75 Lateral Face 15 x 5 5 x 5= 25 5 x 5= 25 15 x 5= 75 75 + 75 + 75 + 75 + 25 + 25 15 x 5= 75 350

12 x 5 = 60 12 x 5 = 60 12 x 9= 75 Times 2 426 5 x 9= 75 Times 2

Two are 12 x 9 Two are 5 x 9 Two are 12 x 5

Two are 3 x 5 Two are 5 x 2 Two are 3 x 2

A B c D E F

2 x 3 = 6 cm² 5 x 3 = 15 cm² A B c 2 x 3 = 6 cm² D 2 x 5 = 10 cm² E 5 x 3 = 15 cm² F 2 x 5 = 10 cm²

62 2 x 3 = 6 cm² 5 x 3 = 15 cm² 2 x 3 = 6 cm² 2 x 5 = 10 cm²

He incorrectly drew the net He incorrectly drew the net. Faces D and F should have been 2 cm by 5 cm, not 3 cm by 5 cm. If Emilio tried to fold his net into a prism, he would have found that the 2-cm sides of faces A and C do not line up with faces D or F.