Çözüldü Square Prism Volume - Two Variable Equations

If a square prism-shaped board has three painted white surfaces and three painted red surfaces, with areas of 76 and 12 square units, respectively, what is the volume of the board in cubic units?

Lengths of the edges: a, b, b
3·a·b = 12 ⇒ a·b = 4....(I)
2b^2 + a·b = 12....(II)
Substituting the value in (I) for its place in (II), b = 6 units....(III)
Moving the value of b in (III) to (I) yields a = 2 / 3 unit....(IV)
The volume of the board using the values in (III) and (IV) is a·b·b = (2 / 3)·6·6 = 24 square units.

Turkish version of the original question:
Üç yüzeyi beyaza, diğer üç yüzeyi ise kırmızıya boyanan kare dik prizma biçimli tahtanın beyaz ve kırmızı renkli toplam alanları sırasıyla 76 ve 12 birimkare ise tahtanın hacmi kaç birimküptür?