1. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Page 657
13)
Cube
8 Vertices: S, T, U, V, W, X, Y, Z
12 Edges: 𝑺𝑻 , 𝑻𝑼 , 𝑼𝑽 , 𝑽𝑺 , 𝑺𝑾 , 𝑻𝑿, 𝑼𝒀 , 𝑽𝒁 , 𝑾𝑿 , 𝑿𝒀 ,
𝒀𝒁 , 𝒁𝑾
2 Bases seen; Possible to have 6 bases
14)
Rectangular Pyramid
5 Vertices: A, B, C, D, E
8 Edges: 𝑨𝑩 , 𝑩𝑪 , 𝑪𝑫 , 𝑫𝑬 , 𝑨𝑬 , 𝑩𝑬, 𝑪𝑬 , 𝑫𝑬
1 Base; ABCD
15)
Cylinder
No Vertices; No edges; Base R and Base Q
16)
Pentagonal Prism
17)
Triangular Pyramid
18)
19)
Square
20)
Rectangle
21)
20)
Rectangle
21)
40) D
41) F
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

2. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

3. Representations of 3-D Figures
Section 10–2
Geometry PreAP, Revised ©2014
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

4. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Definitions
There are many ways to represent a three dimensional object. An orthographic drawing shows six different views of an object: top, bottom, front, back, left side, and right side.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

5. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Example 1
Draw all six orthographic views of the given object. Assume there are no hidden cubes.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

6. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Your Turn
Draw all six orthographic views of the given object. Assume there are no hidden cubes.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

7. Section 10–3 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us
Surface Area of Prisms
Section 10–3
Geometry PreAP, Revised ©2014
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

8. Surface Area vs. Lateral Surface Area
The surface area of a 3-D figure is the sum of the areas of all the faces or surfaces that enclose the solid.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

9. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Definitions
Prisms have 2 congruent parallel bases
A lateral face is not a base. The edges of the base are called base edges.
A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles.
An oblique prism has at least one nonrectangular lateral face.
Height is between the two bases
An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases.
Surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas side faces (not including the bases)
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

10. Area Formulas for Prisms
Lateral Area of a Right Prism: L = Ph where P is perimeter of the figure and h is height
Surface Area of a Right Prism: S = Ph + 2B where B is the base area (The surface area formula is only true for right prisms. To find the surface area of an oblique prism, add the areas of the faces)
Surface Area of a Cube: S = 6s2 where s stands for side length
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

11. To find Lateral Surface Area
As a net of the rectangular prism is shown below:
Height of Prism A B C D
Perimeter of the Base
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

12. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Example 2
Find the lateral and total surface area of the shape.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

13. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Example 2
Find the lateral and total surface area of the shape.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

14. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Example 3
Find the lateral area and surface area of a cube with edge length 8 cm.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

15. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Your Turn
Find the lateral area and surface area of a cube with edge length 8 cm.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

16. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Example 4
Find the dimensional change of the rectangular prism with the length and width is 8 yards and the height is 6 yards and the dimensions is being multiplied by 2/3.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

17. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Example 4
Find the dimensional change of the rectangular prism with the length and width is 8 yards and the height is 6 yards and the dimensions is being multiplied by 2/3.
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

18. 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms
Assignment
Page all, all Page , 14, 22, 25, 26, 32
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10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms