SOLUTION: A rectangular prism with a square base has a lateral area of 96 square yards and a surface area of 128 square yards. What is the length of a base edge?

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Question 452526: A rectangular prism with a square base has a lateral area of 96 square yards and a surface area of 128 square yards. What is the length of a base edge?
Answer by pedjajov(51) About Me  (Show Source):
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Rectangular prism with the square as a base has:
- 2 bases, each is square with side a
- 4 lateral faces, each rectangular with 2 sides equal to a (each belonging to the base) and two sides equal to the height of the prism equal to h
:
Area of such base is
B=a%5E2
:
Area of such lateral face is:
F=ah
:
Surface area is sum of all areas of all 6 faces: 2 bases and 4 lateral faces
S=2B%2B4F
S=2a%5E2%2B4ah
:
Lateral area consists of area of four lateral faces:
L=4F
L=4ah
:
So we have:
S=128
L=96
S-L=128-96=32
:
2a%5E2%2B4ah-4ah=32
2a%5E2=32
a%5E2=16
a=sqrt%2816%29
a=4
:
Length of the base edge is 4 yards.