The first things to know are:
Area of triangle= 1/2 x base x height
So, using the provided info., we should break the parallelogram down to a triangle and trapezoid.
FIRST, find the area of the parallelogram (the entire figure). Its area is A=bh.
the base is 6+7=13 meters. The height is 8 meters. 13x8=104 sq. m.
NEXT, Find the area of the triangle. Remember its area is A=1/2bh
That is, the base=6m and the height=8 m. Forget about the hypotenuse! So, 6x8= 48 and 1/2 of that is 24 meters. The triangle's area= 24 sq. m.
LAST, subtract the area of the parallelogram to the area of the triangle. (104 sq.m. - 24 sq. m.)
The area of the shaded region (the trapezoid) is 80 sq. m.