Question

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
...

Answer 1

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}`