Parallelogram - area

Calculate the area of the parallelogram if the sides are a = 80, b = 60 long, and the size of the diagonal angle is 60°.

Correct answer:

S =  2424.91

Step-by-step explanation:

a=80 b=60 F=60 ∘ G=180−F=180−60=120 ∘ a2 = x2+y2−2xy cos(G) b2 = x2+y2−2xy cos(F) a2−b2 = 2xy cos(F)−2xy cos(G) k = xy k=(a2−b2)/2/(cosF−cosG)=(a2−b2)/2/(cos60° −cos120° )=(802−602)/2/(cos60° −cos120° )=(802−602)/2/(0.5−(−0.5))=1400 5000 = x2+(1400/x)2 x1​=20.707 x2​=67.611 y1​=1400/x1​=1400/20.707≐67.61 y2​=1400/x2​=1400/67.611≐20.7067 u1​=2⋅ x1​=2⋅ 20.707=41.414 u2​=2⋅ y1​=2⋅ 67.61≐135.22 s=(a+b+u1​)/2=(80+60+41.414)/2=90.707 S1​=s⋅ (s−a)⋅ (s−b)⋅ (s−u1​)​=90.707⋅ (90.707−80)⋅ (90.707−60)⋅ (90.707−41.414)​≐1212.455 S=2⋅ S1​=2⋅ 1212.455=2424.91

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.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

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

algebraarithmeticplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: