Answer:
[tex]\boxed{A=552in^2}[/tex]
Step-by-step explanation:
The window is shown below, so we have two trapezoids. A trapezoid is a quadrilateral (polygon with exactly 4 sides) where at least one pair of opposite sides are parallel. The area of a trapezoid can be found as:
[tex]A=\frac{(b_{1}+b_{2})h}{2} \\ \\ Where: \\ \\ b_{1} \ and \ b_{2} \ are \ the \ parallel \ sides \ and \ h \ the \ height[/tex]
Since there are two trapezoids and each with identical dimensions, we can find the area of the window by finding the area of one trapezoid and multiplying this result by 2:
[tex]A=2 \times \frac{(b_{1}+b_{2})h}{2} \\ \\ A=(b_{1}+b_{2})h \\ \\ where: \\ b_{1}=30in \\ b_{2}=16in \\ h=12in[/tex]
Finally:
[tex]A=(16+30)\times 12 \\ \\ \therefore \boxed{A=552in^2}[/tex]
