A geometry problem by Kaleem Kħặŋ

Let the entire rectangle have side lengths $x$ and $y$ . The required ratio above can be expressed as:

$\frac{xy - 12 \cdot 16}{12 \cdot 16} = \frac{25}{6}$ ;

or $\frac{xy}{192} = \frac{25}{6} + 1$ ;

or $xy = 192(\frac{31}{6}) = \boxed{992}.$

$R= 12 \times 16 = 192$

---

$\dfrac{G}{R}=\dfrac{25}{6}$

$G=R \times \dfrac{25}{6}$

$G = 192 \times \dfrac{25}{6} = 800$

---

$G + R = 192 + 800 = \boxed{992}$

Red area $=12\times16=192$

Green area $=192\times\dfrac{25}6=800$

Total $=192+800+\boxed{992}$