As shown in the figure, in the right angle trapezoid ABCD, ∠ C = 90 °, ad ‖ BC, AD + BC = AB, e is the midpoint of CD. If ad = 2, BC = 8, calculate the area of △ Abe

As shown in the figure, in the right angle trapezoid ABCD, ∠ C = 90 °, ad ‖ BC, AD + BC = AB, e is the midpoint of CD. If ad = 2, BC = 8, calculate the area of △ Abe

Take the midpoint F of AB and connect EF. From the trapezoidal median linear quality, we know EF ∥ ad, pass a to make Ag ⊥ BC to g, and intersect EF to H. from the theorem of parallel line equal segment, we know ah = GH and ah, GH are perpendicular to ef. In RT △ ABG, from the Pythagorean theorem, we know: ag2 = ab2-bg2 = (AD + BC) 2 - (BC-AD) 2 = 102-62 = 82