Joan’s house has a window in a shape of rectangle surmounted with a semi-circle. For a given perimeter,what are the dimensions o fthe window if it allows the smallest amount of light? the answer is A= P/4+pi (2P/4+pi),,,please need the whole solution.By the way ,this topic is maxima and minima

Ok now lets proceed step by step

Variables: = R = radius of the semicircle, length = l and height = h

Assume semicircle on the length => 2R = l
and the perimeter is known
hence
P = constant =


Now we want to minimize the area (the light that is)
so

to minimize

hence we get the R as

put in the A and get answer