As we know,Pressure = Thrust/Area.
So,Pressure is inversely proportional to Area.
This means that if pressure will increase then area will decrease. If pressure will decrease then area will increase.
One end is kept wider to increase the area , So,less pressure must act on our fingertip when we press it.
And other end is kept sharp,So that pressure acting must be more and thepin could easily get into the board......
Hope this helped u.
Please mark as brainliest answer......