The circumference of a circle is increased by 50%. By what percentage does its area increase?

Step 1. The new radius. $r_{\text{new}} = 1.5\,r$.

Step 2. The new area. $A_{\text{new}} = \pi\,(1.5\,r)^2 = 2.25\,\pi r^2 = 2.25\,A$.

Step 3. The increase. $2.25 - 1 = 1.25$, so the area increases by $125\%$.