Geometry: An Interactive Journey to Mastery

Lesson 28: Tilings, Platonic Solids, and Theorems

3. Twelve congruent equilateral triangles are used to construct a tetrahedron and an octahedron. What is the
   volume of the tetrahedron compared to the volume of the octahedron?


4. Lines are drawn in a unit square, as shown in
   Figure 28.3)LQGDIRUPXODIRUWKHDUHDRIWKH
   shaded inner square in terms of the value x.
   ͼ௘&KHFNWKDW\RXUIRUPXODJLYHVWKHFRUUHFWYDOXHVIRU 1
   x 2 and x 13 .௘ͽ
   x
   x

x

x

íx

íx

íx

íx

Figure 28.3