Parallelogram 82626

Calculate the area of a parallelogram if we know the perimeter is 23 cm, the diagonal is 8.5 cm, and one side is 1.5 cm longer.

Correct answer:

S =  16.2068 cm2

Step-by-step explanation:

o=23 cm u=8.5 cm a = 1.5 + b  o=2(a+b) a=1.5+b 23=2(a+b) a=1.5+b  23=2 (a+b) a=1.5+b  2a+2b=23 ab=1.5  Row221 Row1Row2 2a+2b=23 2b=10  b=210=5 a=2232b=2232 5=6.5  a=213=6.5 b=5  u2= (a+x)2+h2 b2= x2+h2  u2b2=(a+x)2+x2  8.5252=(6.5+x)2+x2 2x213x+5=0 2x2+13x5=0  a=2;b=13;c=5 D=b24ac=13242(5)=209 D>0  x1,2=2ab±D=413±209 x1,2=3.25±3.614208 x1=0.364208074 x2=6.864208074  x=x1=0.36420.3642 cm  h=b2x2=520.364224.9867 cm  S=2a h=26.5 4.9867=16.2068 cm2

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