Question

the perimeter of a plane figure is the total distance around the figure. find the perimeter of the figure below.

Explanation:

Step1: Identify side - lengths

The side - lengths of the figure are $3\frac{1}{8}$ feet, $5$ feet, $3\frac{1}{8}$ feet, $15\frac{3}{4}$ feet, $\frac{9}{2}$ feet, $15\frac{3}{4}$ feet.

Step2: Convert mixed - numbers to improper fractions

$3\frac{1}{8}=\frac{3\times8 + 1}{8}=\frac{25}{8}$, $15\frac{3}{4}=\frac{15\times4+3}{4}=\frac{63}{4}$, $\frac{9}{2}=\frac{36}{8}$ (after getting a common denominator of 8 for addition).

Step3: Add the side - lengths

\[

$$\begin{align*} &\frac{25}{8}+5+\frac{25}{8}+\frac{63}{4}+\frac{36}{8}+\frac{63}{4}\\ =&\frac{25 + 25+36}{8}+5+\frac{63 + 63}{4}\\ =&\frac{86}{8}+5+\frac{126}{4}\\ =&\frac{43}{4}+5+\frac{126}{4}\\ =&\frac{43+126}{4}+5\\ =&\frac{169}{4}+5\\ =&\frac{169}{4}+\frac{20}{4}\\ =&\frac{169 + 20}{4}\\ =&\frac{189}{4}=47\frac{1}{4} \end{align*}$$

\]

Answer:

$47\frac{1}{4}$