Answer:
Area of parallelogram = 432 [tex]cm^2[/tex].
Length of [tex]\overline{AC}[/tex]= 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= [tex]base\times height[/tex]
Pythogorous theorem :
[tex](perpendicular\; side)^2+ (Base)^2= ( hypotenuse)^2[/tex]
[tex](BC)^2= (AB)^2+ (AC)^2[/tex]
[tex](30)^2=(18)^2+ (AC)^2[/tex]
900=324+[tex](AC)^2[/tex]
[tex](AC)^2[/tex]=900-324=576
AC=[tex]\sqrt{576}[/tex]=24 cm
Length of side AC=24 cm
Area of parallelogram = [tex]18\times 24[/tex]=432 [tex]cm^2[/tex].
In II figure
AD=26 cm
DB=10 cm
AB=BC ( given)
By using pythogorous theorem
In triangle ABD
[tex](AD)^2= (BD)^2+ (AB)^2[/tex]
[tex](26)^2= (10)^2+ (AB)^2[/tex]
676=100 +[tex](AB)^2[/tex]
[tex](AB)^2[/tex]= 676-100=576
AB=[tex]\sqrt{576}[/tex]
AB=24 cm
AC= [tex]2\times AB[/tex]
AC= [tex]2\times 24[/tex]
AC=48 cm .
