A square prism with base perimeter is 16 cm and height is 8cm.
a) What is the length of one edge of the base.
b) What is the lateral surface area.
c) What is the base area.
d) What is the total surface area.
e) What is the volume.
Answers
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.
Usually, if "right" or "oblique" is not mentioned, you can assume the prism is a right prism.
The general formula for the lateral surface area of a right prism 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
Lateral Surface Area =12(8)=96 inches2
The general formula for the total surface area of a right prism 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.
There is no easy way to calculate the surface area of an oblique prism in general. The best way is to find the areas of the bases and the lateral faces separately and add them.
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 12h(b1+b2) .
B=12(4)(6+12)=36 cm2
T.S.A.=ph+2B =28(10)+2(36) =280+72=352 cm2