SOLUTION: Prism M has a length of 5 units, width of 5 units, and height of 10 units. If the length, width, and height of Prism N are triple that of Prism M, then what is the surface area of

Question 280648: Prism M has a length of 5 units, width of 5 units, and height of 10 units. If the length, width, and height of Prism N are triple that of Prism M, then what is the surface area of Prism N?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Prism M has characteristics:
L = length = 5
W = width = 5
H = height = 10
.
We will assume the terms length, width, and height have the usual meanings.
.
Prism N has dimensions that are triple those of Prism M:
l = 3L = 3*5 = 15
w = 3W = 3*5 = 15
h = 3H = 3*10 = 30
.
We assume the prism is solid, so...
The surface area of Prism N includes the areas of the three sides and the areas of the two ends:
.
The area of the sides is simply 3 * surface area of a single side.
Each side is just a rectangle, so the area = length * width.
a = l*w = 15*15 = 225 units squared
3a = 3*225 = 675 units squared.
.
The area of each of the ends = area of a triangle = 1/2*base*height
We will define base = width.
.
e = 1/2*15*30 = 1/2*450 = 225 units squared
.
There are two ends, so 2e = 450 units squared
.
Total surface area = 3a + 2e = 675 + 450 = 1125 units squared
.
Done.
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