Finding the Area of ABMN: A Geometry Problem

In summary, the conversation discusses finding the area of the NCD and ABMN in a rectangle ABCD where M is the midpoint of BC and AC intersects MD at N. The solution includes finding the areas of MCB and ABC in terms of AB and BC, and using a coordinate system and linear equations to find the height of MNC. The conversation also briefly mentions using this method to prove that primes of the form 4n+1 are infinite.
  • #1
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In the figure, ABCD is a rectangle. M is the midpoint of BC and AC intersects MD at N.
Find the Area of the NCD: Area of ABMN.

I am sorry i don't know how to solve this question. Thanks.
 

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  • #2
Well you can find areas of MCB and ABC easy enough in terms of lengths AB and BC (I'm assuming your answer neads to be in terms of AB and BC-so I would label them x and y to make it easier) Then the only trick would be finding the area of MNC, you can find the base easy enough the height is the tricky part. Once you know the area of MNC finding NCB and ABMN should be simple.

As far as finding the height of MNC I might try creating a coordinate system for the figure then finding linear equations for the lines AC and MD then solving the two equations simultaneously to find their point of intersection.
 
  • #3
In fact, the ans is 2:5. And I can calculate this question by using your method. Thank.
 
  • #4
Your welcome. And that's true for any rectangle? How interesting.
 
  • #5
  • #6
tamalkuila said:
prove that primes of the form 4n+1 are infinite?send the proof to tamalkuila@gmail.com
What does this have to do with the original question?

The Bob (2004 ©)
 

1. What is the formula for finding the area of ABMN?

The formula for finding the area of ABMN is A = (1/2) * b * h, where b is the base and h is the height.

2. How do I determine the base and height of ABMN?

The base of ABMN is any side of the quadrilateral, and the height is the perpendicular distance from the base to the opposite side.

3. Is ABMN a special type of quadrilateral?

Yes, ABMN is a parallelogram, which means that opposite sides are parallel and equal in length.

4. Can I use the Pythagorean theorem to find the height of ABMN?

Yes, if the quadrilateral is a right trapezoid, you can use the Pythagorean theorem to find the height by using the lengths of the two bases and one of the legs.

5. What units should I use when finding the area of ABMN?

The units for the base and height should be consistent. For example, if the base is measured in inches, the height should also be in inches. The area will then be in square inches.

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