#### Answer

a) $3\frac{5}{16}$
b) $29\frac{1}{16}$

#### Work Step by Step

Before adding or subtracting fractions, convert the denominators of each fraction to the lowest common denominator by multiplying the numerator and the denominator by the same number. Add or subtract the numerators, keeping the denominator at the same value.
To find the length of the missing segment, identify the labeled segment(s) that combine with the segment whose dimension is missing to make up a larger segment whose dimension is given. Subtract the dimensions of the smaller segment(s) from the longer length to find the missing dimension.
$?=5\frac{9}{16}-(1\frac{1}{8}+1\frac{1}{8})=5\frac{9}{16}-(1\frac{1\times2}{8\times2}+1\frac{1\times2}{8\times2})=5\frac{9}{16}-(1\frac{2}{16}+1\frac{2}{16})$
$=5\frac{9}{16}-2\frac{4}{16}=3\frac{5}{16}$
To then find the perimeter, sum the dimensions of each of the segments that make up the edges of the figure.
$P=5\frac{1}{16}+4\frac{3}{8}+2\frac{1}{16}+7\frac{11}{16}+1\frac{1}{8}+2\frac{5}{32}+3\frac{5}{16}+2\frac{5}{32}+1\frac{1}{8}$
$=5\frac{1\times2}{16\times2}+4\frac{3\times4}{8\times4}+2\frac{1\times2}{16\times2}+7\frac{11\times2}{16\times2}+1\frac{1\times4}{8\times4}+2\frac{5}{32}+3\frac{5\times2}{16\times2}+2\frac{5}{32}+1\frac{1\times4}{8\times4}$
$=5\frac{2}{32}+4\frac{12}{32}+2\frac{2}{32}+7\frac{22}{32}+1\frac{4}{32}+2\frac{5}{32}+3\frac{10}{32}+2\frac{5}{32}+1\frac{4}{32}$
$=27\frac{66}{32}=29\frac{2}{32}=29\frac{1}{16}$