What is the area of the shaded region in the figure above?

51 m^2

Step-by-step explanation:

Draw a vertical line through the roof peak.  There is a trapezoid on either side.  The average height of the trapezoid is (16 m + 10 m)/2 = 13 m.  The width of one trapezoid is 2.5 m.  Thus, the area of one trapezoid is

(13 m)(2.5 m) = 32.5 m^2.

There are two such trapezoids, so the combined area is 2(32.5 m^2), or 65 m^2.

Now find the area of the open door:  It is (7 m)(2 m) = 14 m^2.

Subtracting this door area from the overall area:  

65 m^2 - 14 m^2 = 51 m^2

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