They took a prism of six faces and denoted its length, breadth and height by l, b and h respectively. The faces of the prism except the bases are shown below.
The faces of the prism, except its two bases, are:
ABHE, DCGF, ADFE and BCGH
All the faces are rectangular and each surface has an area:
Area of the face ABHE (A1) = l × h = lh
Area of the face DCGF (A2) = l × h = lh
Area of the face ADFE (A3) = b × h = bh
Area of the face BCGH (A4) = b × h = bh
Sum of the areas of all these faces:
= A1 + A2 + A3 + A4
= lh + lh + bh + bh
= 2lh + 2bh
= 2h (l + b) = 2 (l + b) × h = P × h (where P = perimeter of the base)
So, the sum of the areas of all faces except the two bases is the lateral surface area of the prism.
Lateral surface area of the prism (LSA) = 2h (l + b)
Also, Lateral surface area of prism (LSA) = P × h