Table of Contents

Last modified on October 26th, 2024

The surface area of a rectangular prism is the entire space occupied by its outer layer (or faces). It is expressed in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}.

Like all 3-dimensional shapes, we can calculate 2 types of surface areas in a rectangular prism.

The total surface area (*TSA*) of a rectangular prism is the sum of the lateral surface area and twice the base area. The formula to calculate the* TSA* of a rectangular prism is given below:

The lateral surface area (*LSA*) of a rectangular prism is only the sum of the surface area of all its faces except the bases. The formula to calculate the total and lateral surface area of a rectangular prism is given below:

Now, let us derive the formulas to calculate the surface areas of a rectangular prism.

The total surface area of a rectangular prism is calculated by adding the areas of all 6 rectangular faces.

Let us consider a rectangular prism with l = length, w = width, and h = height.

Here,

The total surface area of the rectangular prism = area of [6 rectangular faces]

= area of [ABCD + EFGH + CDEF + ABGH + ADEH + BCFG]

Now,

The area of ABCD = l × w = lw

The area of EFGH = l × w = lw

The area of CDEF = w × h = wh

The area of ABGH = w × h = wh

The area of ADEH = l × h = lh

The area of BCFG = l × h = lh

Thus,

**The total surface area (TSA) of the rectangular prism**

= area of [ABCD + EFGH + CDEF + ABGH + ADEH + BCFG]

= lw + lw + wh + wh + lh + lh

= 2lw + 2wh + 2lh

= **2(lw + wh + lh)**

The lateral surface area of a rectangular prism is calculated by adding the areas of all its side faces except the bases (top and bottom faces).

Thus,

**The lateral surface area (LSA) of the rectangular prism**

= TSA – The area of the top and bottom faces

= 2(lw + wh + lh) – area of [ABCD + EFGH]

= 2(lw + wh + lh) – 2lw

= 2(wh + lh)

**= 2h(w + l)**

Here are some examples to help you understand the concept better.

**Find the surface area of a rectangular prism given in the figure.**

Solution:

As we know,

Total Surface Area* (TSA) = 2(lw + wh + hl) , *here *l* = 15 m, *w* = 7 m, *h *= 5 m

∴ *TSA *= 2(15 × 7 + 7 × 5 + 5 × 15)

= 430 cm^{2}

**Find the lateral surface area of a rectangular prism whose length is 9.5 cm, width is 8 cm, and height is 4 cm.**

Solution:

As we know,

Lateral Surface Area* (LSA) = 2(wh + hl),* here *w *= 8 cm, *h *= 4 cm, *l* = 9.5 cm

∴ *LSA *= 2{(8 × 4) + (4 × 9.5)}

= 140 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 October 26th, 2024