In the diagram above, ADF is a right triangle. BCED is a square with

Statement #1: angle DCF = 75 degrees

We know that angle DCE = 45 degrees. (diagonal bisects the right angle; BCDE is a square).

Angle ECF = 75-45 = 30 degrees
Now because CEF = 90 degrees; Therefore Angle EFC = 60 degrees.

Also because ADF is a right angled triangle, Angle DAF = 90 - 60 = 30 degrees.

Now because I know angles; I can get EF and AB.

CEF is a 30-60-90 triangle. Its sides are in a ratio of 1: \sqrt{3}: 2. We know CE = 12. We can get EF. (No need to calculate. This is DS)
Once EF is known, DF (base of bigger triangle is known; DF = DE+EF)

Similarly, we can also get AB. ABC is also a 30-60-90 triangle. BC is parallel to DF and so angle BCA = angle EFC = 60 degrees.

Once AB is known, AD is also known.

Area of complete triangle is known. (0.5 AD * DF)

Sufficient


Statement #2: AB:EF = 3[/color]

Say Ab = 3x, then EF will be x
Triangles ABC and CEF are similar. (Angles are same.)

Therefore by triangle property:

\(\frac{AB}{CE}\) = \(\frac{BC}{EF}\)

\(\frac{3x}{12}\) = \(\frac{12}{x}\)

x is known.

Again Base of triangle and Height is known. Area can be calculated.

Sufficient.

D is the Answer.