Table of Contents

Last modified on August 3rd, 2023

chapter outline

 

Surface Area of a Hexagonal Prism

The surface area (or total surface area) of a hexagonal 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 Hexagonal Prism

Let us solve some examples to understand the concept better.

Solved Examples

Find the lateral and the total surface area of a hexagonal prism with a base edge of 5 cm, an apothem of 4.33 cm, and a height of 6 cm.

Solution:

As we know,
Lateral Surface Area (LSA) = 6bh, here b = 5 cm, h = 6 cm
∴ LSA = 6 × 5 × 4
= 120 cm2
Total Surface Area (TSA) = 6ab + LSA, here a = 4.33 cm, b = 5 cm
∴ TSA = 6 × 4.33 × 5 + 120
= 249.9 cm2

Finding the lateral and total surface area of a hexagonal prism when the BASE EDGE and HEIGHT are known

Find the total surface area of a hexagonal prism with a base edge of 4 cm and a height of 7.5 cm.

Solution:

Here we will use an alternative formula
Total Surface Area (TSA) = ${6bh+3\sqrt{3}\times b^{2}}$, here b = 4 cm, h = 7.5 cm
${\therefore TSA=6\times 4\times 7.5+3\sqrt{3}\times 4^{2}}$
≈ 263 cm2

Finding the surface area of a hexagonal prism when BASE PERIMETER and HEIGHT are known

Find the total surface area of a hexagonal prism with a base perimeter of 42 cm and a height of 10.3 cm.

Solution:

As we know,
Total Surface Area (TSA) = 2 × Base Area + P × h
Now, Perimeter (P) = 6s, here P = 42 cm
s = ${\dfrac{P}{6}}$
= ${\dfrac{42}{6}}$
= 7 cm
Now, base area (B) = area of hexagon
${\therefore B=\dfrac{3\sqrt{3}}{2}\times s^{2}}$, here s = 7 cm
${=\dfrac{3\sqrt{3}}{2}\times 7^{2}}$
= 127.3 cm2
∴ B = 127.3 cm2
∴Total Surface Area (TSA) = 2B + Ph, here h = 10.3 cm
∴TSA = 2 × 127.3  + 42 × 10.3
= 687.2 cm2

Last modified on August 3rd, 2023

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