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 a−b=1.5  Row2−21​⋅ Row1→Row2 2a+2b=23 −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

Our quadratic equation calculator calculates it.


Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
See also our trigonometric triangle calculator.

You need to know the following knowledge to solve this word math problem:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: