Answer:
[tex]116.82\:\text{square inches}[/tex]
Step-by-step explanation:
The window consists of a large square and 4 smaller triangles on the outside. The side length of this square is marked as 10, and therefore the area of this square is [tex]10^2=100\:\mathrm{in^2}[/tex].
The area of a triangle is given by [tex]\frac{1}{2}\cdot b\cdot h[/tex]. Since the problem states that the overlapping squares are congruent, both legs of the triangle will be [tex]2.9[/tex] and intersect at a [tex]90^{\circ}[/tex] angle.
Thus, the sum of all four triangles is [tex]\frac{1}{2}\cdot 2.9\cdot 2.9\cdot 4=16.82\:\mathrm{in^2}[/tex].
Therefore, the area of the window is:
[tex]100+16.82=\boxed{116.82\:\mathrm{in^2}}[/tex]
