Esercizi svolti per il libro Matematica.blu: Algebra, Geometria, Statistica, Vol. 1
Soluzione
DH=CK=xDH=CK=xDH=CK=x; AD=BC⇒AH=BK=xAD=BC \rArr AH=BK=xAD=BC⇒AH=BK=x; AB=AH+HK+KB=x+y+x=2x+yAB=AH+HK+KB=x+y+x=2x+yAB=AH+HK+KB=x+y+x=2x+y; CD=KH=yCD=KH=yCD=KH=y.
Area del trapezio ABCD=(AB+CD)⋅DH2ABCD=\dfrac{(AB+CD) \cdot DH}{2}ABCD=2(AB+CD)⋅DH === (2x+y+y)⋅x2\dfrac{(2x+y+y) \cdot x}{2}2(2x+y+y)⋅x === (2x+2y)⋅x2\dfrac{(2x+2y) \cdot x}{2}2(2x+2y)⋅x === 2(x+y)⋅x2\dfrac{\cancel2(x+y)\cdot x}{\cancel2}22(x+y)⋅x === x(x+y)=x2+xyx(x+y)=x^2+xyx(x+y)=x2+xy.