MHB Change a Pentagon into a Triangle with Equal Area

AI Thread Summary
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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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