] The area of trapezoid TRAP is 100. Furthermore, TR = 32, AP = 8, and TP = RA. If ∠T = ∠R, what is the length of segment TP?
Let H be the foot of the perpendicular from T to RA. Since T and R are congruent angles, triangles THP and RHA are congruent, so PH=HA=1/2*AP=4. The area of trapezoid TRAP is 1/2*(TR+AP)(PH+HA)=1/2*(32+8)(4+4)=100, so TP=RA=10.