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Use similar triangles

You might need: Calculator


In the diagram below, DR is perpendicular to OP.
Triangle A D P and triangle D U O, where point D is between point P and O on segment P O, and points A and U are on the same half-plane relative to line P O. Angle A P D is a right angle. Ray D R bisects angle A D U. A dashed line segment intersects segment D O at a right angle at point M. It has endpoints M and U. Side M O is four units. Side D M is ten units. Side D P is three point seventy-five units.
Find the area of DUO.
If entering your answer as a decimal, round your final answer to the nearest hundredth.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
square units