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Last modified on August 3rd, 2023

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 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 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*) = 6*bh,* here *b* = 5 cm, *h* = 6 cm

∴ *LSA *= 6 × 5 × 4

= 120 cm^{2}

Total Surface Area (*TSA*) = 6*ab* + *LSA*, here *a* = 4.33 cm, *b* = 5 cm

∴ *TSA* = 6 × 4.33 × 5 + 120

= 249.9 cm^{2}

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 cm^{2}

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 cm^{2}

∴ *B* = 127.3 cm^{2}

∴Total Surface Area (*TSA*) = 2B + Ph, here *h* = 10.3 cm

∴*TSA* = 2 × 127.3 + 42 × 10.3

= 687.2 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 August 3rd, 2023