the lateral area and the total area for each of cube and cuboid

Question

a cuboid whose total area =132cm and lateral = 112

Answer 1

If cuboid dimensions are L by W by H then the total area is 2(LW+LH+WH)=132cm².

Lateral area is 2(WH+LH)=2H(L+W)=112cm². Therefore 132-112=20cm²=2LW, LW=10cm².

LW+LH+WH=66cm², LH+WH=56cm²=H(L+W).

However, lateral area can also be 2L(W+H)=2W(L+H), depending on orientation of the cuboid.

So 2LW+2LH=2LW+2WH, therefore L=W, and L=W=√10cm. 2LH=56, LH=28cm² and H=28/√10cm.

So the dimensions could be H=8.85cm, L=W=3.16cm.