Question

The figure below is made from squares given the area of the figure find its perimeter to the nearest tenth. A=90ft squared

Answer 1

As the figure is made for 6 squares, the total area of the figure divided into 6 is the area of one square:

`\begin{gathered} A_F=90ft^2 \\ \\ A_S=(90ft^2)/(6)=15ft^2 \end{gathered}`

The area of one square is 15 square feet.

The area of a square is equal to the square lenght

`A=l^2`

Then, as the given squares have area of 15 square feet the measure of the lenght of one square is:

`\begin{gathered} 15ft^2=l^2 \\ \sqrt[]{15}ft=l \end{gathered}`

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:

`\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}`

Then, the perimeter of the figure is 14.5 feet