Table of Contents

Last modified on August 3rd, 2023

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 m^{2}, cm^{2}, mm^{2}, or in^{2}.

The general formula to find the total surface area of a prism is:

**Total Surface Area ( TS**

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:

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.

**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 cm^{2}

**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*) = 6*ab* + *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 cm^{2}

**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 cm^{2}

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on August 3rd, 2023