Geometry

Question Analysis
This reverse-calculation problem tests algebraic manipulation of surface area formulas.

Key Concept Explanation
The TSA formula for square pyramids can be rearranged to solve for base side length.

Step-by-step explanation
TSA = base area + lateral area
340 = s² + 2 × P × 12 = s² + 2 × 4 × s × 12
Simplify equation:
s² + 24s - 340 = 0
We need to find two numbers that multiply to - 340 and add up to 24.
We can write  and .
So, .
Set each factor equal to zero:If 

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