Answer:
[tex]5\dfrac{1}{2}\ cm[/tex]
Step-by-step explanation:
The perimeter of the shown figure is the sum of the lengths of all sides. So, the perimeter is
[tex]AE+ED+DC+CB+AB[/tex]
Using commutative and reflexive properties, rewrite it as follows:
[tex](AE+DC)+DE+BC+AB[/tex]
Therefore, the perimeter is
[tex]P\\ \\=1\dfrac{1}{5}+1 \dfrac{1}{4}+1\dfrac{3}{10}+1\dfrac{3}{4}\\ \\=(1+1+1+1)+\left(\dfrac{1}{5}+\dfrac{3}{10}\right)+\left(\dfrac{1}{4}+\dfrac{3}{4}\right)\\ \\=4+\left(\dfrac{2}{10}+\dfrac{3}{10}\right)+1\\ \\=5+\dfrac{5}{10}\\ \\=5+\dfrac{1}{2}\\ \\=5\dfrac{1}{2}\ cm[/tex]
