MHB Change a Pentagon into a Triangle with Equal Area

Click For 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: 118

Thread 'Significant figures for inherently bound values'

I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
View full post »

Similar threads

MHB What is the Maximum Area of an Inscribed Pentagon with Perpendicular Diagonals?
  • · Replies 1 ·
Replies
1
Views
1K
MHB [ASK] Find the ratio of the area of triangle BCH and triangle EHD
  • · Replies 4 ·
Replies
4
Views
2K
B Find triangles with areas that are integers
  • · Replies 20 ·
Replies
20
Views
4K
MHB Divide ABCDE into two parts with equal area
  • · Replies 6 ·
Replies
6
Views
2K
MHB Area of Triangle ABC Given Dimensions
  • · Replies 5 ·
Replies
5
Views
2K
MHB Calculating Perimeter & Area of a Parallelogram & Triangle
  • · Replies 1 ·
Replies
1
Views
1K
MHB What is the Minimal Area of a Right-Angled Triangle with an Inradius of 1 Unit?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Area of Triangle ABC: Find the Answer Here
  • · Replies 2 ·
Replies
2
Views
1K
MHB ASVAB circle and inscribed rectangle area problem
  • · Replies 6 ·
Replies
6
Views
1K
MHB Area of Triangle ABC: Find the Solution
  • · Replies 2 ·
Replies
2
Views
2K