take a rectangle a by b.
for change in temp del T,the linear expansions be p and q along a and b..
A=ab.. change in area be del A
try to draw a picture yourself..its more convenient
del A= aq+bp+pq (ap=del a,bq=del b)
so del A=ab(p+q).del T pq is neglected as it is negligible..
del A/ A(del T)= p+q which is the coefficient of superficial expansion..
adding we get C