The surface area, also known as the total surface area (TSA) of a prism, is the total space occupied by its flat faces. The surface area is measured in square units such as m2, cm2, mm2, or in2.
Formulas
The general formula to find the total surface area of a prism is:
Total Surface Area (TSA) = 2 × Base Area + Base Perimeter ×Height, here, the height of a prism is the distance between the two bases.
The total surface area of a prism is the combined area of the 2 bases and the areas of the lateral faces.
Since Lateral Surface Area (LSA) of a prism = Base perimeter x height
The lateral surface area is the area of all the faces except the bases.
We can also write:
Total Surface Area (TSA) = 2 × Base Area +LSA
However, there are specific formulas to calculate the surface area of different prisms. They are given below:
Surface Area of a Prism
Some formulas have additional labeling for particular prisms.
In triangular, rectangular, and trapezoidal prisms, ‘l’ (or length) stands for the distance between the bases, and ‘h’ stands for the height of the polygonal base. ‘l’ is the length for a square prism, and ‘a’ represents the four congruent base edges. For pentagonal and hexagonal prisms, ‘a‘ is the apothem, and ‘b’ is the base edge.
Let us solve some examples involving the above formulas to understand the concept better.
Solved Examples
Find the total surface area of a triangular prism whose base edges are 4 cm, 4 cm, 3 cm, height is 3.71 cm, and length is 6 cm.
Solution:
As we know, Total Surface Area (TSA) = b × h + (a + b + c) × l, here a = c = 4 cm, b = 3 cm, h = 3.71 cm, l = 6 cm ∴ TSA = 3 × 3.71 + (4 + 3 + 4) × 6 = 77.13 cm2
Find the total surface area of a hexagonal prism whose base edge is 3 cm, apothem is 2.6 cm and height is 4 cm.
Solution:
As we know, Total Surface Area (TSA) = 6ab + 6bh, here a = 6.5 cm, b = 3 cm, h = 4 cm ∴ TSA = 6 × 2.6 × 3 + 6 × 3 × 4 = 6 × 3(2.6 + 4) = 118.8 cm2
Find the total surface area of a rectangular prism with a length of 7 cm, a width of 4 cm, and a height of 5 cm.
Solution:
As we know, Total Surface Area (TSA) = 2(lw + wh + lh), here l = 7cm, w = 4cm, h = 5 cm ∴ TSA = 2(7 × 4 + 4 × 5 + 7 × 5) = 166 cm2
Find the total surface area of a hexagonal prism whose base edge is 3 cm, apothem is 2.6 cm and height is 4 cm.