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 36m and the sides of whose base are 51,37 and 20m, 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

Comments

comments