If you connect points B and D, and draw a line starting from D to a point (say X) on segment AB such that DX is parallel to AE and perpendicular to AB, the entire region ABCDE is divided into the following three parts:

Part 1: Rectangle AXDE w/ sides 8 (AE or XD) and 2 (DE or AX), area=8*2 = 16

Part 2: Right angle triangle BDX w/ sides 8 (XD), 6 (XB) and hypotenuse BD = 10
area = (1/2)*8*6=24

Part 3: Isosceles triangle BDC w/ sides 13 (BC and CD) and base BD=10 (from Part 2, see above). The altitude of this triangle is 12 (The altitude divides base into half, so we have to find the side of a right angle triangle with side 5 and hypotenuse 13, the answer is 12)
area=(1/2)*10*12=60

So toal area = 16+24+60 = 100 answer