38. Platonic Solids There are five regular polyhedrons. They are called regular because all their faces are congruent regular polygons, and the same number of faces meet at each vertex. They are also called Platonic solids after the Greek philosopher Plato, who first described them in his work Timaeus (about 350 B.C.).

    

    Tetrahedron

    

    Hexahedron

    

    Octahedron

    

    Dodecahedron

    

    Icosahedron

    1. Match each net below with a Platonic solid.
       1. 
       2. 
       3. 
       4. 
       5. 
    2. The first two Platonic solids have more familiar names. What are they?
    3. Verify that Euler's Formula is true for the first three Platonic solids.
39. A cube has a net with area 216  in . 2 . 216 , in , . squared , . How long is an edge of the cube?
40. Writing Cross sections are used in medical training and research. Research and write a paragraph on how magnetic resonance imaging (MRI) is used to study cross sections of the brain.

C Challenge

41. Open-Ended Draw a single solid that has the following three cross sections.

    

    Horizontal

    

    Vertical

Visualization Draw a plane intersecting a cube to get the cross section indicated.

42. scalene triangle
43. isosceles triangle
44. equilateral triangle
45. trapezoid
46. isosceles trapezoid
47. parallelogram
48. rhombus
49. pentagon
50. hexagon

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