Quoted from ThePinballCo-op:

Math teacher here. I'm assuming bigger = volume. A ball that's twice as big is not also twice the surface area.
You have to take the volume of Earth and multiply that by 2.4 first, find the radius, then take the surface area of your new planet (using S/V = 3/R) and multiply that by 0.31.
Earth's current volume = 259,875,159,532 mi³
New Earth volume = 623,700,382,877 mi³
New Earth radius = 5300.24323572 mi
New Earth total surface area = 353,021,751 mi²
31% = 109,436,742 mi²
Which is also what RonaldRayGun got but in a different way, and he showed his work. Full credit.

Quoted from bobmathuse:

OK, people, calm down. There's a terminology gap here. NASA refers to exoplanets' sizes in terms of multiples of earth's RADIUS, not VOLUME. That means you have to use the 2.4 times radius logic, not volume, so the exoplanet's surface area would be 2.4^2 times that of earth, i.e. a multiple of 5.76.
The reason NASA does it this way is that most people have difficulty understanding what "twice the size" means when construed as volume. If you were asked to create a ball "twice the size of a baseball" using volume, you'd struggle with it. Twice the size using radius you'd just measure and go.
As for the application here, a lot of science fiction writers have written about "world building", plus there have been hundreds of panels on it at conventions in the past 80 years (I attended a large number of these). Have you used any of those resources? Take a look at Murasaki or Medea for starters.
Of course for real surface area, try Ringworld (Larry Niven) or a Dyson Sphere.