Given:

∠BEC = 90°

∠DAE = 90°

CD = AE = 8cm

BE = 15cm

BC = 17cm

Consider ΔCEB

Here, By Pythagoras theorem

BC² = CE² + EB²

17² = CE² + 15²

CE² = 17² – 15²

CE² = 289 – 225 = 64

CE = 8

Here,

∠AEC = 90°

CD = CE = 8cm

∴ AECD is a Square.

∴ Area (Trap. ABCD) = Area (Sq. AECD) + Area (ΔCEB)

Area (Trap. ABCD) = AE×EC + 1/2×CE×EB

Area (Trap. ABCD) = 8×8 + 1/2×8×15 = 64 + 60 = 104cm²

∴ Area (Trap. ABCD) = 124cm²