Answer:
30
Step-by-step explanation:
Perimiter is the length of each side added up. We don't know the side lengths, but we can find it.
It tells us the volume and height, and we use the side lengths to find volume, so lets use that. I'm not sure how you have learned how to find the area of a pentagon, but I am going to use the formula google shows. I am going to use x for the side length
A = sqrt(25+10sqrt(5))x^2/4
Now, for any right prism you take the volume of you get the area of the base and multiply it by the height So we can work that out to find the sides.
A*h = V
(sqrt(25+10sqrt(5))x^2/4)*14 = 840
(sqrt(25+10sqrt(5))x^2/4) = 60 (Divide both sides by 14)
sqrt(25+10sqrt(5))x^2 = 240 (Multiply both sides by 4)
x^2 = 34.874 (Divide both sides by sqrt(25+10sqrt(5))
x = 5.905 (square root of both sides)
Now we have the length of one side. Since there are five sides we multiply that by 5.
5 * 5.905 = 29.525 So it rounds up to 30.
Let me know if there is something you did not understand.
