SOLUTION: Hi, I'm struggling with this test question that I'm really confused on: "In triangle ABC, angle C is a right angle. Point M is the midpoint of segment AB, point N is the midpoi

Algebra ->  Triangles -> SOLUTION: Hi, I'm struggling with this test question that I'm really confused on: "In triangle ABC, angle C is a right angle. Point M is the midpoint of segment AB, point N is the midpoi      Log On


   

Question 1127456: Hi, I'm struggling with this test question that I'm really confused on:
"In triangle ABC, angle C is a right angle. Point M is the midpoint of segment AB, point N is the midpoint of segment AC and point O is the midpoint of segment AM. The perimeter of triangle ABC is 112 and ON=12.5. What is the area of quadrilateral MNCB?"
Thanks, I would really appreciate some help on this!
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is a right triangle, and a 7-24-25 right triangle doubled (14-48-50) would have perimeter 112.
MN is between the midpoints and is half of the base, which is 14.
That makes MN 7
The quadrilateral is a trapezoid with base 1 14 and base 2 7; height is 12
Area would be (1/2)24(21)=252 square units.