What shape is the football gate?

I tried to figure it out, how 1 tree and two sticks with the length of 2 can form the area more than 4? The largest area would be rectangle. What is the trick on this problem, can anybody explain with Geometry language.

Thanks.

Re: What shape is the football gate?

The key point of the problem statement is

"She knew that the standard football goal was rectangular, but, being creative, she assumed that her goal could have the form of an arbitrary quadrangle."

So, it may be not a rectangle.

Re: What shape is the football gate?

I tried trapezoid like:

/|

2/_|

| |

2|__|

x

and tried to maximize the function - f(x) for total area which answer is sqrt(3) and total area is ~4.33

How to get ~4.8 for the given test?

Re: What shape is the football gate?

Try placing sticks a and b as follows:

#

#`. a

# `.

# `.

x # \

# \ b

# \

# \

=====================

y

Hint: It can be proved that the area is maximal when x = y and angle between a and b is 135 degrees.