Answer:
\(A_{total}=123.3in^{2}\)
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
\(P=6s\\56=6s\\s=\frac{56}{6}=9.3in\)
So, the area of the square is
\(A_{square}=s^{2}=(9.3)^{2} =86.5in^{2}\)
Now, the are of an equilateral triangle is
\(A_{triangle}=\frac{\sqrt{3} }{4}s^{2}\)
Where \(s\) is the side, replacing its value, we have
\(A_{triangle}=\frac{\sqrt{3} }{4}(9.3)^{2}=36.8in^{2}\)
The total are of the composite figure would be the sum of each
\(A_{total}= 86.5+36.8=123.3in^{2}\)
Therefore, the area of the composite shape is
\(A_{total}=123.3in^{2}\)
