Table of Contents

Last modified on September 6th, 2022

The surface area (or total surface area) of a pentagonal prism is the entire amount of space occupied by all its outer surfaces (or faces). It is measured in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}.

The formula is given below:

Let us solve some examples to understand the concept better.

**Find the lateral and the total surface area of a pentagonal prism given in the figure.**

Solution:

As we know,

Lateral Surface Area (*LSA*) = 5*bh*, here *b* = 8 m, *h* = 12 m

∴ *LSA* = 5 × 8× 12

= 480 m^{2}

Total Surface Area (*TSA*) = 5ab + *LSA*, here *a* = 5.505 m, *LSA* = 480

∴ *TSA* = 5 × 5.505 × 8 + 480

= 700.2 m^{2}

** Find the lateral area of a pentagonal prism with a base edge of 5.5 cm and height of 11 cm**.

Solution:

As we know,

Lateral Surface Area (*LSA*) = 5*bh*, here b = 5.5 cm, h = 11 cm

∴ *LSA *= 5 × 5.5 × 11

= 302.5 cm^{2}

Finding the surface area of a pentagonal prism when the **BASE EDGE** and **HEIGHT** are known

**Find the surface area of a pentagonal prism with a base edge of 11 cm and height 6 cm.**

Solution:

As we know,

Total Surface Area (*TSA*) = ${ 5bh+\dfrac{1}{2}\sqrt{5\left( 5+2\sqrt{5}\right) }b^{2} }$ , here b = 11 cm, h = 6 cm

∴ *TSA* = ${ 5\times 11\times 7+\dfrac{1}{2}\sqrt{5\left( 5+2\sqrt{5}\right) }\times 11^{2}}$

= 801.35 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 September 6th, 2022