Answer:
SA = \(2(\frac{lw}{7}+\frac{lh}{7}+\frac{wh}{49})\)
Step-by-step explanation:
The surface area of a rectangular prism is given by :
\(SA=2(wl+hl+hw)\)
Where l stands for length
w stands for width
h stands for height
Given is - If the width and height of a rectangular prism are each shrunk to one seventh of the original size but the length remains the same.
So, length = l
width = \(\frac{w}{7}\)
height = \(\frac{h}{7}\)
The new surface area will be =
SA = \(2(l\times \frac{w}{7} +l\times \frac{h}{7}+ \frac{w}{7}\times \frac{h}{7})\)
Simplifying this we get:
SA = \(2(\frac{lw}{7}+\frac{lh}{7}+\frac{wh}{49})\)
There are many other ways to write this but it has the same meaning, so, we can take this as the answer.
SA = \(2(\frac{lw}{7}+\frac{lh}{7}+\frac{wh}{49})\)
