The relation between the coefficient of linear expansion (α) and the coefficient of area expansion (β) is:

beta = 2alpha

Explanation

• α (alpha) = coefficient of linear expansion
  It tells how much the length of a material changes with temperature.

• β (beta) = coefficient of area expansion
  It tells how much the area of a material changes with temperature.

When a solid plate is heated, it expands in two perpendicular directions (length and breadth).
Since each direction expands with coefficient α, the total area expansion becomes approximately 2α.

Therefore

β=2α

Additional relation (useful for exams)

• γ (gamma) = coefficient of volume expansion

γ=3α