[tex]\text{area}=184\text{ square cm}[/tex]
Explanation
Step 1
to find the total area divide the figure
[tex]\begin{gathered} \text{Area}=4\text{ squares+4 triangles} \\ \end{gathered}[/tex]
now, we need to find the area of the triangle
so, we need to find the hypotenuse of the triangle
[tex]\begin{gathered} \text{hyp}^2=3^2+4^2 \\ \text{hyp}^2=9+16 \\ \text{hyp}^2=25 \\ \sqrt[]{\text{hyp}^2}=\sqrt[]{25} \\ \text{hyp}=5 \end{gathered}[/tex]
so, the height of the triangle is 5 cm
Step 2
let
side of the square=6
heigth of the triangle=5
base of the triangle=6
[tex]\begin{gathered} \text{Area}=4\text{ squares+4 triangles} \\ \text{Area}=4(side^2)\text{+4 }(\frac{b\cdot h}{3}) \\ \text{replace} \\ \text{Area}=4(6^2)\text{+4 }(\frac{6\cdot5}{3}) \\ \text{area}=4(36)+4(10) \\ \text{area}=144+40 \\ \text{area}=184\text{ square cm} \end{gathered}[/tex]
I hope this helps you
