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Answer:
The volume of the pentagonal prism is 1446.25
Step-by-step explanation:
First of all we need to calculate the area of the pentagon
A = area
a = apothem = 8.9
p = perimeter = 13 * 5 = 65
A = (a*p) / 2
A = (8.9 * 65) / 2
A = 578.5 / 2
A = 289.25
To calculate the volume of a pentagonal prism we have to use the following formula:
a = area = 289.25
v = volume
h = height = 5
v = a * h
we replace the values that we know
v =
289.25 * 5
v = 1446.25
The volume of the pentagonal prism is 1446.25
Adults = x
Students = y = x + 40. 40 more student than adult
Adult = $8, Student = $6
Total for Adults = 8*x = 8x
<span>Total for students = 6*y = 6y
</span>
Total = $1920
8x + 6y = 1920
Hence system of equations are:
<span>y = x + 40
</span>
<span>8x + 6y = 1920</span>
