Answer:
![A_{total}=123.3in^{2}](https://tex.z-dn.net/?f=A_%7Btotal%7D%3D123.3in%5E%7B2%7D)
Step-by-step explanation:
If the triangle and the square have the same sides, then that triangle is equilateral, that is, all its sides are the same.
Now, this is a composite shape, where one side of the triangle is on one side of the square, this means that the perimeter is the sum of all 6 sides. So, each side is
![P=6s\\56=6s\\s=\frac{56}{6}=9.3in](https://tex.z-dn.net/?f=P%3D6s%5C%5C56%3D6s%5C%5Cs%3D%5Cfrac%7B56%7D%7B6%7D%3D9.3in)
So, the area of the square is
![A_{square}=s^{2}=(9.3)^{2} =86.5in^{2}](https://tex.z-dn.net/?f=A_%7Bsquare%7D%3Ds%5E%7B2%7D%3D%289.3%29%5E%7B2%7D%20%3D86.5in%5E%7B2%7D)
Now, the are of an equilateral triangle is
![A_{triangle}=\frac{\sqrt{3} }{4}s^{2}](https://tex.z-dn.net/?f=A_%7Btriangle%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7Ds%5E%7B2%7D)
Where
is the side, replacing its value, we have
![A_{triangle}=\frac{\sqrt{3} }{4}(9.3)^{2}=36.8in^{2}](https://tex.z-dn.net/?f=A_%7Btriangle%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%289.3%29%5E%7B2%7D%3D36.8in%5E%7B2%7D)
The total are of the composite figure would be the sum of each
![A_{total}= 86.5+36.8=123.3in^{2}](https://tex.z-dn.net/?f=A_%7Btotal%7D%3D%2086.5%2B36.8%3D123.3in%5E%7B2%7D)
Therefore, the area of the composite shape is
![A_{total}=123.3in^{2}](https://tex.z-dn.net/?f=A_%7Btotal%7D%3D123.3in%5E%7B2%7D)