Area of triangle DUO: A=? Formula of the area of a triangle: A=(1/2)bh Base of the triangle: b Height of the triangle: h
In this case: b=OD=OM+MD=4+10→b=14 h=MU=?
Since DR is perpendicular to OP: Angle RDO = 90° = Angle RDP
Like angle RDU is congruent with angle RDA, the angle UDM must be congruent with angle ADP.
If angle UMO is 90°, the angle UMD is 90° too.
The triangles ADP and UDM have two congruent angles: Angle UMD = 90° = Angle APD Angle UDM = Angle ADP Then the triangles UDM and ADP are similars, and theirs sides must be proportionals: MU/MD=AP/DP Replacing the known values: MU/10=4.5/3.75 MU/10=1.2 Solving for MU. Multiplying both sides of the equation by 10: 10(MU/10)=10(1.2) MU=12
A=(1/2)OD*MU A=(1/2)(14)(12) A=84
Answer: The area of triangle DUO is 84.00 square units.
