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
Messages
1,221
Reaction score
0
ABCDE is a pentagon,now please construct a triangle APQ
,and both of them must have the same area
 
Mathematics news on Phys.org
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
 

Attachments

  • pentagon.jpg
    pentagon.jpg
    19.5 KB · Views: 114
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top