Finding the Area of ABMN: A Geometry Problem

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Homework Help Overview

The problem involves finding the area of a specific region (ABMN) within a rectangle (ABCD) where M is the midpoint of one side, and a diagonal intersects another segment. The subject area is geometry, focusing on area calculation and properties of rectangles.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss calculating areas of triangles and rectangles using lengths and midpoints, with suggestions to use a coordinate system for determining heights and intersections. There is also a mention of labeling dimensions for clarity.

Discussion Status

Some participants have offered guidance on how to approach the problem, particularly in calculating areas and finding heights. There appears to be a mix of interpretations regarding the problem's requirements, and while one participant claims to have a solution, there is no consensus on the method or final answer.

Contextual Notes

One participant expresses uncertainty about the problem's setup, and there are unrelated posts that diverge from the original geometry question, indicating potential confusion or misdirection in the discussion.

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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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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.
 
In fact, the ans is 2:5. And I can calculate this question by using your method. Thank.
 
Your welcome. And that's true for any rectangle? How interesting.
 
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 ©)
 

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