Answer:
88 cm
Step-by-step explanation:
The composite figure is made by arranging four identical rectangles around the side of a square.
The area of the square is [tex]36cm^2[/tex].
So the side length of the square is,
[tex]=\sqrt{36}=6cm[/tex]
The area of each rectangle is [tex]1\dfrac{1}{3}[/tex] of the area of the square.
So the area of each rectangle is,
[tex]=1\dfrac{1}{3}\times 36=\dfrac{4}{3}\times 36=48cm^2[/tex]
As the breadth of each rectangle is equal to the side length of the square i.e 6 cm, so
[tex]\Rightarrow \text{Length}\times\text{Breadth}=\text{Area}[/tex]
[tex]\Rightarrow \text{Length}\times 6=48[/tex]
[tex]\Rightarrow \text{Length}=8cm[/tex]
Then perimeter of the cross pattern figure will be,
[tex]=4\times \text{Perimeter of the rectangle}-\text{Perimeter of the square}[/tex]
[tex]=4\times 2(8+6)-(4\times 6)[/tex]
[tex]=4\times 2(14)-(24)[/tex]
[tex]=4\times 28-24[/tex]
[tex]=88cm[/tex]
