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 are $3\frac{1}{8}$ feet, $4$ feet, $3\frac{1}{8}$ feet, $17\frac{3}{4}$ feet, $17\frac{3}{4}$ feet, and $8\frac{1}{2}$ feet.

Step2: Convert mixed numbers to improper fractions

$3\frac{1}{8}=\frac{3\times8 + 1}{8}=\frac{25}{8}$, $17\frac{3}{4}=\frac{17\times4+3}{4}=\frac{71}{4}$, $8\frac{1}{2}=\frac{8\times2 + 1}{2}=\frac{17}{2}$.

Step3: Find a common denominator

The common denominator of 8, 4, and 2 is 8. So $\frac{71}{4}=\frac{71\times2}{4\times2}=\frac{142}{8}$ and $\frac{17}{2}=\frac{17\times4}{2\times4}=\frac{68}{8}$.

Step4: Add the fractions

$\frac{25}{8}+4+\frac{25}{8}+\frac{142}{8}+\frac{142}{8}+\frac{68}{8}$. First, write 4 as $\frac{32}{8}$. Then $\frac{25 + 32+25+142+142+68}{8}=\frac{434}{8}=54.25$ feet.

Answer:

$54.25$ feet