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 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

Representations of 3-D Figures Section 10–2 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

Section 10–3 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us Surface Area of Prisms Section 10–3 Geometry PreAP, Revised ©2014 viet.dang@humble.k12.tx.us 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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) 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

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. 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms Assignment Page 665 14-16 all, 22-25 all Page 685 13, 14, 22, 25, 26, 32 11/17/2018 12:58 PM 10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms