In my IGCSE textbook, there is a question:
A long time ago Dulani found an island shaped like a triangle with 3 straight shores of length 3 km, 4 km, 5 km. He said nobody could come within 1 km of his shore. What was the area of his exclusion zone?
I know that this is a right angle triangle. By applying $3*1+4*1+5*1+(1^2)*π$ because of three rectangles and exterior angles, I get 15.1 as my answer. How come the answer is 14.8?
The part of the sea that is excluded consists of three rectangular regions along the shoreline, and three circular sectors at the corners. These three circular sectors add up to one full circle. This yields $$3\times1+4\times1+5\times1+\pi\approx15.14...,$$ just as you found. The answer you quote seems incorrect.
The only different interpretation I can imagine is that you should also count part of the interior of the island. But this only increases the area of the exclusion zone.