2025 ESSS P1 Q14

The diagram shows an equilateral triangle \(ABC\) of sides 6 cm.

\(PQRS\) is a rectangle inside triangle \(ABC\) such that \(BP=QC=x\) cm and \(SP=RQ=y\) cm.

1. Show that the area of the shaded region, \(A\text{ cm}^2\), is given by \(A=\sqrt3(9-6x+2x^2)\).[3]
2. Given that \(x\) can vary, find the stationary value of \(A\).[3]
3. Determine if this value of \(A\) is a maximum or minimum.[2]