Question

Find the area of the figure, use pi as 3.14The perimeter of the square in the figure below is 24 inches.

Answer 1

Start by finding the side of the square using the perimeter, a square has 4 equal sides. divide the perimeter by 4

`(24in)/(4)=6in`

now find the area of the square

`\begin{gathered} \\ A=l\cdot l \\ A=6in\cdot6in \\ A=36in^2 \end{gathered}`

continue by finding the area of a whole circles using 3 inches as the radius, because 2 of the form a complete circle.

`\begin{gathered} A=\pi\cdot r^2 \\ A=(3.14)\cdot(3in)^2 \\ A=9\cdot3.14in^2 \\ A=28.26in^2 \end{gathered}`

multiply this by 2 to find the area of the 4 circular sections.

`\begin{gathered} A=2\cdot28.26in^2 \\ A=56.52in^2 \end{gathered}`

Continue by finding the area of the smaller squares, which have a side half of the radius.

`\begin{gathered} A=l\cdot l \\ A=1.5in\cdot1.5in \\ A=2.25in^2 \end{gathered}`

since there are 4 multiply by 4

`\begin{gathered} At=4\cdot2.25in^2 \\ At=9in^2 \end{gathered}`

Finally to find the area of the figure we add the area of the bigger square and the circular portions, and substract the area of the smaller squares.

`\begin{gathered} A_F=(36in^2)+(56.52in^2)-(9in^2) \\ A_F=83.32in^2 \end{gathered}`