Unit 9. Day 12.

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

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= ∙ 2 8 𝑐𝑚 5 𝑐𝑚 40 𝐴= 2 𝑐𝑚 2 𝐴=𝑏∙ℎ 𝐴= ∙ 8 𝑐𝑚 8 𝑐𝑚 𝐴=20 𝑐𝑚 2 𝐴= 64 𝑐𝑚 2

𝑖𝑛 2 Example B: Calculate the surface area of the rectangular prism 18 36 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

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

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 42 4 𝑖𝑛 2 21 2 𝑖𝑛 2 10 1 2 𝑖𝑛 2 𝑆.𝐴.= = = 1 2 =𝑠 𝐴=𝑏∙ℎ 1 2 𝑖𝑛 1 2 𝑖𝑛 𝐴= ∙ 1 4 𝐴= 𝑖𝑛 2