The first figure has 3 angles, the second one has 4 angles, the third one has 5 angles so the next one will have 6 angles.
The violet figures inside stick with each side of the outer figures in the middle, so the last figure will look more less like in the attachment.
The domain of the function that will be derived from the given situation should be restricted to include only the positive integers. This is because we can count the 1/2 or 2/3 or any fraction of a person. Further, there are also no negative number of persons.
7^2+8^2=113
the answer is sqrt(113)