I have this problem with special triangles. I have read the lesson over and over again but I still can't seem to grasp it.Here are some sample...

The given quadrilateral  is AECF , as per the measurement,

AE=12, EC=20, given. CF=AE=12 and FA=EC =20

Therefore, the perimeter= AE+EC+CF+FA=12+20+12+20=64 units.

To find coordinates of R:

The coordinates P qnd Q is known. By distance formula find PQ. Since PQ is known right angled triangle PQR, with angles P=30 and Q=90,  QR  must be  half the  PR.

See the Y  coordinates  of  P and Q . They are same. Therefore, PQ ||  to X axis.

Q being a right angle, QR must be || to Y axis . Therefore the the X cordinate of R remains the same as that of Q , Y cordinate of R is either  Y cordinate of Q  + (1/2)PR or Cordinate of Q - (1/2) PR.