Parallelogram area perimeter

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.

Final 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)  23=2⋅ (a+b) a=1.5+b  2a+2b=23 a−b=1.5  Row2−21​⋅ Row1→Row2 −2b=−10  b=−2−10​=5 a=223−2b​=223−2⋅ 5​=6.5  a=213​=6.5 b=5  u2= (a+x)2+h2 b2= x2+h2  u2−b2=(a+x)2+x2  8.52−52=(6.5+x)2+x2 −2x2−13x+5=0 2x2+13x−5=0  a=2;b=13;c=−5 D=b2−4ac=132−4⋅2⋅(−5)=209 D>0  x1,2​=2a−b±D​​=4−13±209​​ x1,2​=−3.25±3.614208 x1​=0.364208074 x2​=−6.864208074  x=x1​=0.3642≐0.3642 cm  h=b2−x2​=52−0.36422​≐4.9867 cm  S=2a⋅ h​=26.5⋅ 4.9867​=16.2068 cm2

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