Parallelogram 64414

The parallelogram has side a = 58cm and diagonals u = 89cm, v = 52cm. Calculate the perimeter and area of this parallelogram.

Correct answer:

o =  204.2836 cm
S =  2203.1082 cm2

Step-by-step explanation:

a=58 cm u=89 cm v=52 cm  e=u/2=89/2=289=44.5 cm f=v/2=52/2=26 cm  s=2a+e+f=258+289+26=4257=64.25 cm S1=s (sa) (se) (sf)=64.25 (64.2558) (64.2544.5) (64.2526)550.7771 cm2  S1 = 2a h/2  h=4 S1/a=4 550.7771/5837.9846 cm  u2 = (a+x)2+h2  x=u2h2a=89237.9846258=232521722.4871 cm  x2+h2 = b2  b=x2+h2=22.48712+37.9846244.1418 cm  o=2 (a+b)=2 (58+44.1418)=204.2836 cm
S=a h=58 37.98462203.1082 cm2   Verifying Solution:   w=2b+e+f=244.1418+44.5+2657.3209 cm S2=w (wb) (we) (wf)=57.3209 (57.320944.1418) (57.320944.5) (57.320926)550.7771 cm2  S3=2 S1+2 S2=2 550.7771+2 550.77712203.1082 cm2



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