Given the right trapezoid calculate angle ##theta## and the area of triangle ##hat(EAD)##, provided ##EA=4, AB=BC=CD=DA=2, AB_|_EC##?

##/_theta = arctan((sqrt(3)-1)/2)~~0.350879411 rad##

##S_(EAD) = 2##

From right triangle ##Delta ABE##, knowing hypotenuse ##AE=4## and cathetus ##AB=2## we can find another cathetus: ##BE=sqrt(4^2-2^2)=sqrt(12)=2sqrt(3)##.

In the right triangle ##Delta DCE## cathetus ##CD=2##. Second cathetus ##CE = CB+BE = 2+2sqrt(3)##

Now we can determine tangent of angle ##/_ theta##: ##tan(theta) = (CD)/(CE) = 2/(2+2sqrt(3)) = 1/(sqrt(3)+1)=(sqrt(3)-1)/2## Angle ##/_theta## can be determined using an inverse function ##tan^(-1)()## or, as it is often expressed, ##arctan()##: ##/_theta = arctan((sqrt(3)-1)/2)~~0.350879411 rad##

Area of triangle ##Delta EAD## can be calculated using the length of its base ##AD## and altitude ##DC##:

##S_(EAD) = 1/2*AD*DC = 1/2*2*2 = 2##