# Lateral Surface Area of a Prism

The lateral surface area of a prism is the total of the area of the faces.
$\therefore$Lateral Surface Area $= h\left( {AB} \right) + h\left( {BC} \right) + h\left( {CD} \right) + h\left( {DA} \right)$
Lateral Surface Area $= h\left( {AB + BC + CD + DA} \right)$
Lateral Surface Area $=$ Perimeter of the base $\times$ Height of the prism
Lateral Surface Area $=$ Perimeter of the base times the altitude

Rule 1: The lateral area of the prism is equal to the perimeter of the base times the altitude.

Rule 2: Total surface area of a prism is the sum of the lateral areas and the area of its base.

Example:

Find the area of the whole surface of a right triangular prism whose height is $36$m and the sides of whose base are $51,37$ and $20$m, respectively.

Solution:

In all there are five planes figures, i.e., two triangles and three rectangles. Since both the rectangles are of equal area.

Area of both triangles $= \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)}$
Area of both triangles $= \sqrt {54\left( {54 - 51} \right)\left( {54 - 20} \right)\left( {54 - 37} \right)}$
Area of both triangles $= \sqrt {54 \times 3 \times 34 \times 17} = 612$ Square meter
Area of all three Rectangles   $= 36\left( {51 + 20 + 37} \right) = 36 \times 108 = 3888$ Square meter
Area of the whole surface $= 3888 + 612 = 4500$ Square meter