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: The 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 36m and the sides of whose bases are 51,37 and 20m, respectively.

 

Solution:

In all there are five plane 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 meters

Area of all three rectangles    = 36\left( {51 + 20 + 37} \right) = 36 \times 108 = 3888 square meters

Area of the whole surface  = 3888 + 612 = 4500 square meters