Let us draw the height of CH from the top of the obtuse angle.
A quadrangle ABCН is a rectangle, then BC = AH = 3 cm, then the segment DH = AD – AH = 7 – 3 = 4 m.
In a right-angled triangle СНD, the angle СНD = 90, then the angle DСН = 135 – 90 = 45.
Angle СDН = DCН = 45, then triangle СDН is isosceles, СН = DH = 4 cm.
Determine the area of the triangle.
S = (BC + AD) * CH / 2 = (3 + 7) * 4/2 = 20 cm2.
Answer: The area of the trapezoid is 20 cm2.
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