Question

Find the Volume and Surface area

Answer 1

Volume: 203,594

Surface Area: 105,237

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Solve for surface area ✅

Let's start with surface area because it is a bit complex.

`A = 5 ah + (1)/(2) \sqrt{5(5 + 2 √(5))}~a^2`

Now, we must break all of these factors into an equation.

remember, the height is 4, the base is 172

`A = 5 * 172 * 4 + (1)/(2) * \sqrt{5 * (5 + 2 * √(5))} * 172^2`

`A = \sf 1.05237 * 10^5 = 105,237`

So that should wrap things up for surface area, being 105,237

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Solve for volume ✅

Now, we move on to the volume of this pentagonal prism.

`A = (1)/(4) \sqrt{5(5 + 2 √(5))}~a^2h`

Similar to surface area, but different.

`A = (1)/(4) * \sqrt{5 * (5 + 2 * √(5))} * 172^2 * 4`

And the result of this is...

`A = \sf 2.03594 * 10^5`

Which is also equal to ⇒ 203,594

please let me know if this helped or was correct, I really spent a lot of time on this and would like to hear any good or bad feedback. Thanks!