Surface Area of a Prism
The lateral surface area of a prism is the sum of the areas of its lateral faces.
The total surface area of a prism is the sum of the areas of its lateral faces and its two bases.
The general formula for the lateral surface area is L. S. A. = ph where p represents the perimeter of the base and h represents the height of the prism.
Example 1:
Find the lateral surface area of a triangular prism with bases edges 3 inches, 4 inches and 5 inches and altitude 8 inches.
The perimeter is the sum of the bases.
p = 3 + 4 + 5 = 12 inches
T. S. A. = 12(8) = 96 inches2
The general formula for the total surface area is T. S. A. = ph + 2B where p represents the perimeter of the base, h the height of the prism and B the area of the base.
Example 2:
Find the total surface area of an isosceles trapezoidal prism with parallel edges of the base 6 cm and 12 cm, the legs of the base 5 cm each, the altitude of the base 4 cm and height of the prism 10 cm.
The perimeter of the base is the sum of the lengths of the sides.
p = 6 + 5 + 12 + 5 = 28 cm
Since the base is an isosceles trapezoid, its area is 
.
T. S. A. = ph + 2B
= 28(10) + 2(36)
= 280 + 72 = 352 cm2
