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 Ã— 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, â€˜*l*â€™ (or length) stands for the distance between the bases, and â€˜*h*â€™ stands for the height of the polygonal base. â€˜*l*â€™ is the length for a square prism, and â€˜*a*â€™ represents the four congruent base edges. For pentagonal and hexagonal prisms, ‘*a*‘ is the apothem, and â€˜*b*â€™ 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*) =Â *b*Â Ã—Â *h*Â + (*aÂ *+Â *bÂ *+Â *c*) Ã—Â *l*, hereÂ *a*Â =Â *c*Â = 4 cm,Â *b*Â = 3 cm,Â *h*Â = 3.71 cm,Â *l*Â = 6 cm

âˆ´Â *TSA *= 3 Ã— 3.71 + (4 + 3 + 4) Ã— 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*) =Â 6*ab* + *6bh*, hereÂ *aÂ *= 6.5 cm, *b* = 3 cm,Â *hÂ *= 4 cm

âˆ´Â *TSA* = 6 Ã— 2.6 Ã— 3 + 6 Ã— 3 Ã— 4

= 6 Ã— 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*Â +Â *wh*Â +Â *lh*), hereÂ *l*Â = 7cm,Â *wÂ *= 4cm,Â *hÂ *= 5 cm

âˆ´Â *TSA* = 2(7 Ã— 4 + 4 Ã— 5 + 7 Ã— 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