Given that the four triangles are congruent, the total area of the figure is the area of the square plus 4 times the area of one triangle.
Recall that the area of a triangle is given by the formula:
[tex]A=\frac{base*height}{2}.[/tex]
Therefore, the area of one of the triangles is:
[tex]A_{triangle}=\frac{8in*4in}{2}.[/tex]
Simplifying the above result, we get:
[tex]A_{triangle}=16in^2.[/tex]
Now, the area of a square is given by:
[tex]A=side*side.[/tex]
Therefore, the area of the square is:
[tex]A_{square}=4in*4in.[/tex]
Simplifying the above result, we get:
[tex]A_{square}=16in^2.[/tex]
Finally, we get that:
[tex]A_{total}=4A_{triangle}+A_{square}=4*16in^2+16in^2=80in^2.[/tex]
Answer:
[tex]80in^2.[/tex]
