Table of Contents

Last modified on August 3rd, 2023

chapter outline

 

Surface Area of a Pentagonal Prism

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 m2, cm2, mm2, and in2.

Formula

The formula is given below:

Surface Area of a Pentagonal Prism

Let us solve some examples to understand the concept better.

Solved Examples

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

Solution:

As we know,
Lateral Surface Area (LSA) = 5bh, here b = 8 m, h = 12 m
∴ LSA = 5 × 8× 12
= 480 m2
Total Surface Area (TSA) = 5ab + LSA, here a = 5.505 m, LSA = 480
∴ TSA = 5 × 5.505 × 8 + 480
= 700.2 m2

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) = 5bh, here b = 5.5 cm, h = 11 cm
∴ LSA = 5 × 5.5 × 11
= 302.5 cm2

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 cm2

Last modified on August 3rd, 2023

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