False. Since A is any point on PQ, then ar (PAS) ≠ 30 cm2
But, the statement can be true if PA is equal to PS.
Justification:
According to the question,
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm.
Given,
A is any point on PQ
PA<PQ
ar (△PQR) = ½ × PQ × QR
= ½ × 12 × 5
= 30 cm2
PS = 5 cm
Suppose PA<PQ,
ar(△PAS) < ar(△PQR)
ar(△PAS) < 30 cm2
Suppose PA = PQ,
ar (△PAS) = ½ × PQ × PS
= ½ × 12 × 5
= 30 cm2