a surface that consists of 20 equilateral triangles. By what factor does the surface area of an icosahedron increase as the side length of each triangle doubles from a unit to 2a units, if a = 5.5

Answer 1

All areas vary with the characteristic length squared! It doesn't matter the shape of the body or whether you are talking about plane area, surface area, or cross-sectional area as long as you change the length in all cases.

A₂/A₁ =( length₂/length₁)² If you 5 x the radius of a sphere you 5² or 25 times the area. If you triple the side of a cube, you 3² or 9 times the area. Here the important thing is the doubling, the actual a value is irrelevant.