FIND THE AREA OF THE YELLOW RECTANGLE.

GEOMETRIC THEOREMS, TRIGONOMETRIC IDENTITIES, TRIANGULAR RULES, BASIC ARITHMETIC /ALGEBRAIC PROCESSES AND AREA OF RECTANGLE ARE USED TO SOLVED THIS QUESTION.
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[@PS-mh8ts]

At 0:3:23 you'll notice that the word 'theorem' being spelled incorrectly as 'thoerem' causes the text-to-speech translator to mispronounce the word.

[@vikasgoel5182]

Can we assume point o and center of the circle are co-linear. How?

[@Center1ForMathematics]

It is not mandatory that the center of a circle or that of a quarter circle must be labelled O. The point O, in this case, is just a point which lies on the diagonal of the yellow inscribed rectangle. The concept of collinear does not exist or not required in the solution of the given question.

[@PS-mh8ts]

No, it's a serious omission in the problem description. It should have been mentioned that the points F, O, and C are collinear. Usually the letter O is reserved for the center of a circle. If not the center of a circle, O is used to represent a point of symmetry (for example, the meeting point of X and Y coordinates). In this present problem, O is neither the center of the circle, nor the meeting point of the diagonals of the yellow rectangle. This diagram doesn't follow standard conventions.

[@PS-mh8ts]

Quicker method:
Notice that △COE and △CDF are congruent and hence have the same area = (1/2)(CO)(OE)=(1/2)(6)(8)=24 square units. Hence the area of yellow rectangle=2*24=48 square units.

[@Center1ForMathematics]

I like your contructive comment.