satisfy that: 
and natural number 
,
Y by
A paper rectangle 
(
, 
) is folded in such way that vertices 
and 
coincide. What is the area of the obtained pentagon?
(additional problems from Mathematical Kangaroo 2014)
(
, 
) is folded in such way that vertices 
and 
coincide. What is the area of the obtained pentagon?(additional problems from Mathematical Kangaroo 2014)
This post has been edited 1 time. Last edited by parmenides51, Mar 21, 2021, 8:54 AM
![[asy]draw((0,0)--(27.5,0)--(31,4.5)--(13,17)--(-3.5,4.5)--cycle);
draw((13,17)--(27.5,0));
label("A,C",(13,19));
label("B",(33,4.5));
label("D",(-5.5,4.5));
label("E",(29.5,-2));
label("F",(-2,-2));[/asy]](http://latex.artofproblemsolving.com/3/8/5/385d355c39502f9e09d48f24f8460ebd10f75c5b.png)
![[asy]draw((0,0)--(9,0)--(9,3)--(0,3)--cycle);
draw((0,0)--(9,3));
draw((3.75,3)--(5.25,0));
label("A",(-1,0));
label("B",(-0.5,3.5));
label("C",(9.5,3.5));
label("D",(10,0));
label("E",(3.73,3.5));
label("F",(5.25,-0.5));[/asy]](http://latex.artofproblemsolving.com/3/d/4/3d41e6f1a739eb6c91cc3f44aa92f28b01dc6438.png)
.
be 
.
.
,
.
and 
,
Now, let's calculate the area. Examine the first figure. We can split this into two congruent right triangles with legs 
and 
,
and a height of 
.
