Answer:
Area of parallelogram = 432 \(cm^2\).
Length of \(\overline{AC}\)= 48 cm.
Step-by-step explanation:
In the given figure I ABCD is a parallelogram
Base of parallelogram ABCD= AB=18 cm
Length of side BC= 30 cm
We know that
area of parallelogram= \(base\times height\)
Pythogorous theorem :
\((perpendicular\; side)^2+ (Base)^2= ( hypotenuse)^2\)
\((BC)^2= (AB)^2+ (AC)^2\)
\((30)^2=(18)^2+ (AC)^2\)
900=324+\((AC)^2\)
\((AC)^2\)=900-324=576
AC=\(\sqrt{576}\)=24 cm
Length of side AC=24 cm
Area of parallelogram = \(18\times 24\)=432 \(cm^2\).
In II figure
AD=26 cm
DB=10 cm
AB=BC ( given)
By using pythogorous theorem
In triangle ABD
\((AD)^2= (BD)^2+ (AB)^2\)
\((26)^2= (10)^2+ (AB)^2\)
676=100 +\((AB)^2\)
\((AB)^2\)= 676-100=576
AB=\(\sqrt{576}\)
AB=24 cm
AC= \(2\times AB\)
AC= \(2\times 24\)
AC=48 cm .
