why do we use $\pi \cdot d/2+d$ for semicircles I'm in grade seven and right now we are learning perimeter of a semicircle, and I noticed we use the formula $\pi\cdot D/2+D$ (where $D$ is the diameter) instead of $(\pi+2)D/2$, why do we do the first formula instead of the second, where they both have the same answer?

You can use either formula as they are identical, as you've noted.  A reason for preferring the first is that it makes the perimeter calculation explicit: $\pi\cdot D/2$ is the length of the curve, and $+D$ then adds on the straight line across the bottom.
