Question

the perimeter of a plane figure is the total distance around the figure. find the perimeter of the figure below. the perimeter is (type an integer, fraction, or mixed number. simplify your answer.)

Explanation:

Step1: Identify side - lengths

The side - lengths of the figure are $5\frac{1}{8}$ feet, $6$ feet, $5\frac{1}{8}$ feet, $12\frac{3}{4}$ feet, $12\frac{1}{2}$ feet, $12\frac{3}{4}$ feet.

Step2: Convert mixed numbers to improper fractions

$5\frac{1}{8}=\frac{5\times8 + 1}{8}=\frac{41}{8}$, $12\frac{3}{4}=\frac{12\times4+3}{4}=\frac{51}{4}$, $12\frac{1}{2}=\frac{12\times2 + 1}{2}=\frac{25}{2}$.

Step3: Find a common denominator

The common denominator of 8, 4, and 2 is 8. $\frac{51}{4}=\frac{51\times2}{4\times2}=\frac{102}{8}$, $\frac{25}{2}=\frac{25\times4}{2\times4}=\frac{100}{8}$.

Step4: Add the fractions

$\frac{41}{8}+6+\frac{41}{8}+\frac{102}{8}+\frac{100}{8}+\frac{102}{8}= \frac{41 + 6\times8+41+102+100+102}{8}=\frac{41+48 + 41+102+100+102}{8}=\frac{434}{8}$.

Step5: Simplify the fraction

$\frac{434}{8}=\frac{217}{4}=54\frac{1}{4}$ feet.

Answer:

$54\frac{1}{4}$