24814

First I tried through equations to see if any total sides would be the same:

18+15= 33
14+10+9=33
14+4+7+8=33
14+10+1+8=33

Therefore one side of the rectangle is possibly 33 long

18+14= 32
18+4+10=32
15+7+10=32
15+8+9=32
15+7+1+9=32

therefore the other side of the rectange is probably 32 long

7+1 =8 -> the 1 and 7 squares are along the 8 square
9+1 = 10 -> the 9 and 1 squares are along the 10 square
7+8 = 15 -> the 7 and 8 squares are along the 15 square
10+4 = 14 -> the 10 and 4 squares are along the 14 square
8+1 = 9 -> the 8 and 1 squares are along the 9 square
4 + 14 = 18 -> the 4 and 14 squares are along the 18 square

fit them all together and it makes a 32 x 33 rectangle!