Two sides of an isosceles triangle are 10 inches and 20 inches.

The two equal sides must  = 20.......here's why.....by the triangle inequality,  the sum of any two sides of a triangle must be greater than the remaining side....if the two equal sides   =10, then 10 + 10  =  20  which is NOT greater then the remaining side (20)

So....the sides must  be 20, 20  and 10

We can use something known as Heron's Formula to  solve this

First......sum the sides and divide by two  =  (20 + 20 + 10)  / 2  =  25

This is known as the semi-perimeter, S

The area  =   sqrt  [  S * (S -A) * (S -B) * (S-C)  ]    where A, B ,C  are the sides of the triangle

So we have

Area   =sqrt [  (25 * (25  -20) (25 -20) (25 -10) ] = sqrt  [ (25) * (5) (5) (15)] 

Area  =  sqrt  [ 25 * 5 * 5 * 15 ] =

Area  =sqrt [ 9375 ]  ≈  96.8  sq inches