The surface area of a square pyramid can be calculated using the equation

Question

$S=\frac {1}{2}lp+B$ Rearrange the surface area equation for the quantity of interest B

Answer 1

To rearrange the equation for the surface area \( S \) of a square pyramid, given by

\[ S = \frac{1}{2}lp + B, \]

where \( l \) is the slant height, \( p \) is the perimeter of the base, and \( B \) is the area of the base, we want to isolate \( B \).

1. Start with the original equation: \[ S = \frac{1}{2}lp + B. \]

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

This gives us the rearranged equation for \( B \): \[ B = S - \frac{1}{2}lp. \]

Answer 2

Thats wrong

Answer 3

Let's carefully go through the rearrangement of the equation for surface area again.

The surface area \( S \) of a square pyramid is given by the equation:

\[ S = \frac{1}{2}lp + B, \]

where:

• \( S \) is the total surface area,
• \( l \) is the slant height,
• \( p \) is the perimeter of the base,
• \( B \) is the area of the base.

To isolate \( B \), we'll follow these steps:

1. Start with the original equation: \[ S = \frac{1}{2}lp + B. \]

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

This is indeed the correct rearrangement for \( B \).

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