The diagram shows a rectangle, ABCD, where AB = 20 cm and BC = 16 cm. PQRS

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The diagram shows a rectangle, ABCD, where AB = 20 cm and BC = 16 cm.
PQRS is a quadrilateral where PB = AS = 2x cm, BQ = x cm and DR = 4xcm.

a. Express the area of PQRS in terms of x.

b. Given that x can vary, find the value of x for which the area of PQRS is a minimum and find the magnitude of this minimum area.

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