Given a pentagon ABCDE, construct the points T,R,Q,U such that the segments AT, AR, AQ, and AU divide the pentagon into five equal area pieces. (Using straight edge and compass. But you may divide a segment into a number of equal segments for free.)

Solution

Extend CD to a line. Draw BB’ // AC and EE’ // AD. divide B’E’ into 5 equal segments. draw TC’ // AC and UD’ // AD. Draw AT, AR ,AQ, AU and you’re done ! Thank you @MatthewArcus!

Given a pentagon ABCDE, construct the points T,R,Q,U such that the segments AT, AR, AQ, and AU divide the pentagon into five equal area pieces. (Using straight edge and compass. You may divide a segment into a number of equal segments) https://t.co/VhxDk1vlTT By @MarshallWBuck pic.twitter.com/0vtMLrV8Tr

— Mirangu (@Mirangu1) April 2, 2024