#### Answer

a)$\frac{31}{32}$in.
b) 16$\frac{5}{16}$ in.

#### Work Step by Step

Label diagram as ABCDEF
a) Length of missing dimension EF = DC – AB
= 3$\frac{9}{32}$ in. - 2$\frac{5}{16}$ in.
= $\frac{105}{32}$ - $\frac{37}{16}$
= $\frac{105}{32}$ - $ \frac{37}{16} \times$ $\frac{2}{2}$
=$\frac{105}{32}$ - $\frac{74}{32}$
=$\frac{31}{32}$in.
b) Perimeter of the figure = AB+BC+CD+DE+EF+FA
= 2$\frac{5}{16}$in + 2$\frac{1}{2}$in + 2$\frac{3}{8}$in + 3$\frac{9}{32}$in + 2$\frac{3}{8}$in + $\frac{31}{32}$in + 2$\frac{1}{2}$in
= $\frac{37}{16}$ + $\frac{5}{2}$ + $\frac{1}9{8}$+$\frac{105}{32}$ + $\frac{19}{8}$ + $\frac{31}{32}$i + $\frac{5}{2}$
=$\frac{37}{16}$ + $\frac{10}{2}$ + $\frac{38}{8}$+$\frac{136}{32}$
= $ \frac{37}{16} \times$ $\frac{2}{2}$ + $ \frac{10}{2} \times$ $\frac{16}{16}$ + $ \frac{38}{8} \times$ $\frac{4}{4}$ + $\frac{136}{32}$
=$\frac{74}{32}$ + $\frac{160}{32}$ + $\frac{152}{32}$+$\frac{136}{32}$
=$\frac{522}{32}$
=$\frac{261}{16}$
=16$\frac{5}{16}$ in