Two composite shaped external cloaks are proposed based on the concept of linear transformation method and complementary media. Each composite shaped cloak is sub-divided into regions of rectangular and triangular shapes. The advantage of the proposed cloak designs is that the material properties are finite, homogeneous and non-singular within all sub-regions of the cloaks which is good for practical realization. The cloak size of each of the proposed designs is smaller compared to the conventional external cloaks. Moreover the cloaking area of proposed cloaks can be increased in the vertical direction without any change in material parameters of core and complementary regions which is an additional benefit for hiding long objects. Full-wave simulations reveal that the proposed cloaks have good performance even for hiding multiple objects of different shapes and sizes inside it for all angles of incidence of electromagnetic wave.