Questions: Just output the content of the question, DO NOT output additional information or explanations.

Solution Steps

The given lengths of sides are mixed numbers. Let's convert them to improper fractions.

\(4\frac{7}{16} = \frac{4 \times 16 + 7}{16} = \frac{64+7}{16} = \frac{71}{16}\) inches \(8\frac{7}{8} = \frac{8 \times 8 + 7}{8} = \frac{64+7}{8} = \frac{71}{8}\) inches

The figure is a hexagon, and we are given the lengths of all sides. The perimeter is the sum of the lengths of all sides.

Perimeter = \(3 \times \frac{71}{16} + 2 \times \frac{71}{8}\) = \(\frac{213}{16} + \frac{142}{8}\) = \(\frac{213}{16} + \frac{284}{16}\) = \(\frac{497}{16}\)

To convert the improper fraction \(\frac{497}{16}\) to a mixed number, we divide 497 by 16. \(497 \div 16 = 31\) with a remainder of 1. So, \(\frac{497}{16} = 31\frac{1}{16}\)

Final Answer The perimeter of the figure is \( \boxed{31\frac{1}{16}} \) inches.