1. Unit 9. Day 12.

2. CCSS.MATH.CONTENT.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms

3. Example A: Calculate the surface area of the square pyramid.
𝑆.𝐴.=
64 𝑐𝑚 2 +
20 𝑐𝑚 2 +
20 𝑐𝑚 2 +
20 𝑐𝑚 2 +
20 𝑐𝑚 2
𝑆.𝐴.=144 𝑐𝑚 2
𝐴= 𝑏∙ℎ 2
𝐴= 1 2 ∙𝑏∙ℎ
𝐴= ∙
8 𝑐𝑚
5 𝑐𝑚 40 𝐴=
𝑐𝑚 2
𝐴=𝑏∙ℎ
𝐴= ∙
8 𝑐𝑚
8 𝑐𝑚
𝐴=20 𝑐𝑚 2 𝐴= 64
𝑐𝑚 2

5. 𝑖𝑛 2 Example B: Calculate the surface area of the rectangular prism 1836 36 72 + 72
𝑖𝑛 2
252
𝐴=𝑏∙ℎ
𝐴=𝑏∙ℎ
𝐴=𝑏∙ℎ
𝐴= ∙
6 𝑖𝑛
3 𝑖𝑛
𝐴= ∙
12 𝑖𝑛
3 𝑖𝑛
𝐴= ∙
12 𝑖𝑛
6 𝑖𝑛 𝐴= 18
𝑖𝑛 2 𝐴= 36
𝑖𝑛 2 𝐴= 72
𝑖𝑛 2

6. Example C: Imagine that a piece of the rectangular prism is removed
Example C: Imagine that a piece of the rectangular prism is removed. Determine the surface area of both pieces. 18 18 36 9 36 9 72 9 + 72 9 18
𝑖𝑛 2
252
252 𝑖𝑛 2 + 18
72 𝑖𝑛 2 72
𝑖𝑛 2
𝐴=𝑏∙ℎ
𝐴=𝑏∙ℎ
𝐴=𝑏∙ℎ
𝐴= ∙
3 𝑖𝑛
3 𝑖𝑛 =
𝐴= ∙ +
3 𝑖𝑛
3 𝑖𝑛
𝐴= ∙
6 𝑖𝑛
324 𝑖𝑛 2
3 𝑖𝑛 𝐴= 9
𝑖𝑛 2 𝐴= 9
𝑖𝑛 2 𝐴= 18
𝑖𝑛 2

7. Example D: In the diagram, there are 𝟏𝟒 cubes glued together to form a solid. Each cube has a volume of 𝟏 𝟖 𝐢 𝐧 𝟑 . Find the surface area of the solid
42 1
𝑉=𝑙∙𝑤∙ℎ
1 4 𝑖𝑛 2
𝑆.𝐴.= 42 ∙ 3
1 8 =𝑠∙𝑠∙𝑠
1 8 = 𝑠 3 3
𝑖𝑛 2
𝑖𝑛 2
𝑖𝑛 2
𝑆.𝐴.= = =
1 2 =𝑠
𝐴=𝑏∙ℎ
1 2 𝑖𝑛
1 2 𝑖𝑛
𝐴= ∙
1 4 𝐴=
𝑖𝑛 2