Trapezoid OPQR has one vertex at the origin. What is the area of OPQR

Lets extend RQ till Y-axis , and this extension meets y-axis at pt A.
Thus coordinate of A = (0,a)
Now as O is the orgin the co-ordinate of O =(0,0)

now, in in triangle AOR & APQ,
angle A is same for both & PQllOR (as the figure is trapezoid) & AR=2AQ(given)
Thus by triangle properties AO=2AP.......................................................................Please closely refer the diagram provided in the Q-stem

Thus AR = 2a, AQ=a & AO=a & AP=a/2

Area of trapezoid = area of triangle ARO - area of triangle AQP = \(\frac{1}{2}*AR*AO\) - \(\frac{1}{2}*AQ*AP\) =\(\frac{1}{2}*2a*a\) - \(\frac{1}{2}*a*\frac{a}{2}\) = \(a^2\) - \(\frac{a^2}{4}\) = \(\frac{3a^2}{4}\)......Hence the answer is C