Find the area of trapezoid $DUCK$ shown below. [asy] unitsize(2mm); defaultpen(linewidth(.7pt)+fontsize (10pt)); pair D=(0,0), U=(5,12), C=(20,12), K=(36,0), F=(5,0); draw(D--U--C--K--cycle); draw(U--F, linetype("8 4")); draw(rightanglemark(U, F,K,25)); label("$D$",D, SW); label("$U$",U, N); label("$C$",C, NE); label("$K$",K, SE); label("5",midpoint(D--F),S); label("13",midpoint(D--U),NW); label("15",midpoint(U--C),N); label("20",midpoint(C--K),NE); [/asy]

Nina has prepared the following two-column proof below. she is given that ∠oln ≅ ∠lno and she is trying to prove that ol ≅ on. triangle oln, where angle oln is congruent to angle lno step statement reason 1 ∠oln ≅ ∠lno given 2 draw oe as a perpendicular bisector to ln by construction 3 ∠leo ≅ ∠neo transitive property of equality 4 m∠leo = 90° definition of a perpendicular bisector 5 m∠neo = 90° definition of a perpendicular bisector 6 le ≅ en definition of a perpendicular bisector 7 δole ≅ δone side-angle-side (sas) postulate 8 ol ≅ on cpctc nina made two errors in the proof. identify and correct the errors.