Change a Pentagon into a Triangle with Equal Area

Albert

Well-known member
ABCDE is a pentagon,now please construct a triangle APQ
,and both of them must have the same area

Prove It

Well-known member
MHB Math Helper
Re: change the shape of a pentagon into a triangle with equal area

Are we assuming this is a regular pentagon?

Albert

Well-known member
Re: change the shape of a pentagon into a triangle with equal area

Are we assuming this is a regular pentagon?
it may not be a regular pentagon

Prove It

Well-known member
MHB Math Helper
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...

Albert

Well-known member
Hope you can upload a diagram ,so we can see it clearly