The surface area of a square pyramid can be calculated using the equation S=12lp+B%0D%0A𝑆%0D%0A=%0D%0A1%0D%0A2%0D%0A𝑙%0D%0A𝑝%0D%0A+%0D%0A𝐵%0D%0A . Rearrange the surface area equation for the quantity of interest B%0D%0A𝐵%0D%0A .(1 point)

Answer 1

To rearrange the surface area equation for \( B \) (the area of the base of the square pyramid), we start with the equation for the surface area \( S \):

\[ S = \frac{1}{2} l p + B \]

Here, \( l \) is the slant height, \( p \) is the perimeter of the base, and \( B \) is the area of the base.

To isolate \( B \), we can rearrange the equation as follows:

1. Subtract \(\frac{1}{2} l p\) from both sides: \[ B = S - \frac{1}{2} l p \]

So the rearranged equation for the area of the base \( B \) is:

\[ B = S - \frac{1}{2} l p \]