Answer:
[tex]A_{f}[/tex]≅0.034[tex]L^{2}[/tex]
Step-by-step explanation:
The graph shows a rectangle and 8 dodecahedrons but a dodecahedron inscribed in a square is seen, so it is enough to calculate the fractions of areas between the square and the dodecahedron
Square area [tex]A_{s}=0.134L^{2}[/tex]
Area of a right triangle [tex]A_{rt}=\frac{(0.232L*0.134L)}{2}[/tex]
Area fraction [tex]A_{f}=4A_{c}+8A_{rt}\\A_{f}=4*(0.134L)^{2}+8*\frac{0.232L*0.134L}{2} =0.017956L^{2}+0.015544L^{2}[/tex]
[tex]A_{f}[/tex]≅0.034[tex]L^{2}[/tex]
Note: The fractions of the sides of the square and the right triangle are determined by assigning values to L
