ANSWER
The area of the shaded portion is 104 in²
EXPLANATION
The total area of the metal is:
[tex]A_{metal}=18\times6=108in[/tex]
To find the area of the shaded portion we have to subtract the areas of the triangles.
Each triangle is a right isosceles triangle - because there are two angles with the same measure, 45º - so we can say that the base and the height of the triangles are the same:
[tex]b=h[/tex]
The area of one triangle is:
[tex]A_{\text{triangle}}=\frac{b\times h}{2}=\frac{b\times b}{2}=\frac{b^2}{2}[/tex]
By the pythagorean theorem, the base of each triangle is:
[tex]\begin{gathered} 2^2=b^2+h^2 \\ 2^2=b^2+b^2^{} \\ 4=2b^2 \\ b^2=\frac{4}{2} \\ b^2=2 \end{gathered}[/tex]
Replacing into the expression for the area of one
