Since our box consists of 2 identical squares and 4 identical rectangles, we will write a formula for its surface area as the following sum.
A_(Surface)=2A_(Square)+4A_(Rectangle)A_(Square) follows the standard formula for the area of a square. A square's height and length are the same, so multiplying them to find the area is the same as squaring. Let's substitute the given box measurements into it.
A_(Square)= a^2
A_(Square)= 4^2=16
The A_(Rectangle) is similar to the standard formula for the area of a square, because it also is a function of length times height. We know one measurement of the rectangle, the length l, because it shares a side with the square. Let's substitute the given box measurements into it.
A_(Rectangle)= l h
A_(Rectangle)= 4 h
Now, we will substitute what we have into the formula for surface area and simplify.
