MHB Change a Pentagon into a Triangle with Equal Area

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To construct a triangle APQ with the same area as pentagon ABCDE, it's important to clarify whether the pentagon is regular or irregular. The discussion suggests dividing the pentagon into three triangles to calculate the area accurately using the formula 1/2 * ab * sin(C). Participants express a need for visual aids, such as diagrams, to enhance understanding of the construction process. The conversation emphasizes the importance of area calculations in transforming shapes while maintaining equal areas. Clear communication and visual representation are essential for solving this geometric problem effectively.
Albert1
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ABCDE is a pentagon,now please construct a triangle APQ
,and both of them must have the same area
 
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Re: change the shape of a pentagon into a triangle with equal area

Are we assuming this is a regular pentagon?
 
Re: change the shape of a pentagon into a triangle with equal area

Prove It said:
Are we assuming this is a regular pentagon?
it may not be a regular pentagon
 
Well I would be inclined to split the pentagon into three triangles, you should be able to find the area of each triangle using \displaystyle \begin{align*} \frac{1}{2}ab\sin{(C)} \end{align*} or some other method...
 
Hope you can upload a diagram ,so we can see it clearly
,I will upload mine later
 

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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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