MHB Find the ratios of the areas of the four regions

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The discussion focuses on finding the area ratios of four regions formed in square ABCD by point M, the midpoint of side CD. It highlights that triangles MPC and APB are similar, which is crucial for determining the area ratios. Participants suggest using properties of similar triangles to derive the necessary ratios. The conversation emphasizes the importance of justification in the calculations to ensure accuracy. Overall, the goal is to clearly establish the area ratios of ∆MPC, ∆BPC, ∆APB, and quadrilateral APMD.
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In square ABCD point M is the midpoint of side CD. Find the ratios of the areas of the four regions (∆MPC, ∆BPC, ∆APB, and quadrilateral APMD) that are formed. Justify your result.View attachment 8047
 

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Re: Having a difficult time figuring out how to solve this

Hello, and welcome to MHB! (Wave)

I think my first step would be to explain how $\triangle MPC$ and $\triangle APB$ are similar, from which we can determine the ratio of their areas...
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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