As the figure is made for 6 squares, the total area of the figure divided into 6 is the area of one square:
[tex]\begin{gathered} A_F=90ft^2 \\ \\ A_S=\frac{90ft^2}{6}=15ft^2 \end{gathered}[/tex]
The area of one square is 15 square feet.
The area of a square is equal to the square lenght
[tex]A=l^2[/tex]
Then, as the given squares have area of 15 square feet the measure of the lenght of one square is:
[tex]\begin{gathered} 15ft^2=l^2 \\ \sqrt[]{15}ft=l \end{gathered}[/tex]
Then, as each side of each square is square root of 15 feet you have the next:
The perimeter of the figure is the sum of all the sides: The figure has 12 sides: 2 sides have a measure of 2square root of 15 feet and the other 10 sides have a measure of square root of 15 feet:
[tex]\begin{gathered} P=2(2\sqrt[]{15})ft+10(\sqrt[]{15})ft \\ \\ P=4\sqrt[]{15}ft+10\sqrt[]{15}ft \\ \\ P=14\sqrt[\square]{15}ft \\ \\ P=14.491ft\approx14.5ft \end{gathered}[/tex]
Then, the perimeter of the figure is 14.5 feet
