Answer:
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.
[tex]A = 5 ah + \frac{1}{2} \sqrt{5(5 + 2 \sqrt{5})}~a^2[/tex]
Now, we must break all of these factors into an equation.
remember, the height is 4, the base is 172
[tex]A = 5 * 172 * 4 + \frac{1}{2} * \sqrt{5 * (5 + 2 * \sqrt{5})} * 172^2[/tex]
[tex]A = \sf 1.05237 * 10^5 = 105,237[/tex]
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.
[tex]A = \frac{1}{4} \sqrt{5(5 + 2 \sqrt{5})}~a^2h[/tex]
Similar to surface area, but different.
[tex]A = \frac{1}{4} * \sqrt{5 * (5 + 2 * \sqrt{5})} * 172^2 * 4[/tex]
And the result of this is...
[tex]A = \sf 2.03594 * 10^5[/tex]
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!
