# 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:

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
âˆ´ LSA = 6 Ã— 5 Ã— 4
= 120 cm2
Total Surface Area (TSA) = 6ab + LSA, here a = 4.33 cm, b = 5 cm
âˆ´ TSA = 6 Ã— 4.33 Ã— 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
${\therefore TSA=6\times 4\times 7.5+3\sqrt{3}\times 4^{2}}$
â‰ˆ 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 Ã— Base Area + P Ã— 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
âˆ´ B = 127.3 cm2
âˆ´Total Surface Area (TSA) = 2B + Ph, here h = 10.3 cm
âˆ´TSA = 2 Ã— 127.3Â  + 42 Ã— 10.3
= 687.2 cm2

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