Since it took me a long time to understand the above reply (kudos given), my clarification:

\(\text{Area of a Triangle}: \frac{1}{2} \times \text{base} \times \text{height}\)

\(ADC\) and \(BDC\) share a base (\(DC\)).

\(ADC\) and \(BDC\) have the same height as we can determine \(AD\) and \(BC\) are parallel (due to the two right angles).

Therefore areas of \(ADC\) and \(BDC\) are equal.

(1) The area of ΔAED is 16.

The area of ADC = BDC (given above).

Using visual area subtraction

AED = ADC - DEC

BEC = BDC - DEC

Therefore the area of AED = BEC.

Sufficient(2) The area of ΔDEC is 12.

This information cannot be used to obtain anything more as we cannot determine side lengths or angles from the information.

Insufficient(A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

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