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8.8.PS-13

Find the surface area of the
regular hexagonal prism.
3.5 cm
The surface area is cm Superscript 2
4 cm
11 cm
...

8.8.PS-13 Find the surface area of the regular hexagonal prism. 3.5 cm The surface-example-1

1 Answer

5 votes

Answer:

348 cm²

Explanation:

In this problem, we are asked to find the surface area of the regular hexagonal prism. We can use the formula:


SA = 2A + (P \cdot h)

where
A is the area of the prism's hexagonal faces,
P is the perimeter of the hexagonal faces, and
h is the prism's height.

We can solve for the area of the hexagonal faces by splitting it into 6 triangles and multiplying the area of each triangle by 6.


A = 6\left((1)/(2) bh\right)

where
b is the triangle's base and
h is the triangle's height.


A = 6\left((1)/(2)\cdot 4 \cdot 3.5\right)


A = 6\left(2 \cdot 3.5\right)


A = 12 \cdot 3.5


A = 42\text{ cm}^2

We can solve for the perimeter by multiplying one side length by 6.


P = 6(4) = 24\text{ cm}

We are given that the height of the prism is 11 cm.


h = 11\text{ cm}

Finally, we can solve for the surface area of the prism by plugging these values into the above formula.


SA = 2A + (P \cdot h)


SA = 2(42) + (24 \cdot 11)


SA = 84 + 264


\boxed{SA = 348 \text{ cm}^2}

User Pawinder Gupta
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