The diagram shows a trapezium $OPQR$, where $OR=6$ cm and \(\angle OPQ=\angle PQR=\frac{\pi

Question

The diagram shows a trapezium $OPQR$, where $OR=6$ cm and $\angle OPQ=\angle PQR=\frac{\pi}{2}$ radians. $\angle ROP=\theta$ radians, where $\theta$ is acute. $T$ is a point on $PQ$ such that $\angle ORT=\frac{\pi}{2}$ radians and $RT=3$ cm. Show that the area of the trapezium $OPQR$ is $9 \sin 2\theta + 18 \sin^2 \theta \cdot$[3] Given that $\theta$ can vary, find the exact value of $\theta$ for which the area of trapezium $OPQR$ is stationary.[3] Determine whether this value of $\theta$ gives a maximum or minimum value of the area.[2]

Accepted Answer

(b) $\theta =\frac{3\pi }{8}$ (c) Maximum value of the area.

2023 SCGS 4AM CA2 Q6

2023 SCGS 4AM CA2 Q6