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Understanding Polygons and Three-Dimensional Figures: Properties and Calculations

In this lesson, we explore polygons by identifying them through their number of sides and calculating their perimeters. We'll classify polygons as regular or irregular based on their properties. Additionally, we will delve into three-dimensional figures such as polyhedrons, prisms, and pyramids, identifying their bases, faces, edges, and vertices. We will also learn to find the surface area and volume of various solids, including cylinders, cones, and spheres. Practical examples will be provided to enhance understanding.

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Understanding Polygons and Three-Dimensional Figures: Properties and Calculations

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  1. Warm-up Problems • Name polygon A by its number of sides. 2. Name polygon B by its number of sides. • Find the perimeter of polygon A. • Find the perimeter of polygon B. • Classify the polygons as regular or irregular. Lesson 7 Menu

  2. Identify three-dimensional figures. • Find surface area and volume. • polyhedron • regular prism • pyramid • regular polyhedron • Platonic solids • cylinder • cone • sphere • surface area • volume • face • edges • prism • bases • vertex Lesson 7 MI/Vocab

  3. Identify Solids A.Identify the solid. Name the bases, faces, edges, and vertices. Lesson 7 Ex1

  4. Answer: rectangular prism;Bases: rectangles EFHG, ABDCFaces: rectangles FBDH, EACG, GCDH, EFAB, EFGH, ABCD Vertices:A, B, C, D, E, F, G, H Identify Solids The bases are rectangles. This solid is a rectangular prism. Lesson 7 Ex1

  5. Identify Solids B.Identify the solid. Name the bases, faces, edges, and vertices. Lesson 7 Ex1

  6. Answer: hexagonal prism;Bases: hexagon EFGHIJ and hexagon KLMNOPFaces: rectangles EFLK, FGML, GHMN, HNOI, IOPJ, JPKE Vertices:K, L, M, N, O, P, E, F, G, H, I, J Identify Solids The bases are hexagons. This solid is a hexagonal prism. Lesson 7 Ex1

  7. Identify Solids C.Identify the solid. Name the bases, faces, edges, and vertices. Lesson 7 Ex1

  8. Identify Solids The base is a circle and there is one vertex. So, it is a cone. Answer:Base: circle TVertex:Wno faces or edges Lesson 7 Ex1

  9. Identify the solid. • A • B • C • D A. triangular pyramid B. pentagonal prism C. rectangluar prism D. square pyramid Lesson 7 CYP1

  10. Lesson 7 KC1

  11. π π π π π . cm2 . Surface Area and Volume A.Find the surface area of the cone. Answer: The cone has a surface area of 75.4 cm2. Lesson 7 Ex2

  12. π π . π . cm3 Surface Area and Volume B. Find the volume of the cone. Answer: The cone has a volume of 37.7 cm3. Lesson 7 Ex2

  13. Surface Area and Volume The amount of material used to make the tube would be equivalent to the surface area of the cylinder. Lesson 7 Ex3

  14. . Surface Area and Volume Answer: Mike needs about 405 square inches of cardboard for each tube. Lesson 7 Ex3

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