Parallelogram 5027

Calculate the area of the parallelogram if the side sizes are a = 80, b = 60, 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=180F=18060=120 a2 = x2+y22xy cos(G) b2 = x2+y22xy cos(F) a2b2 = 2xy cos(F)2xy cos(G) k = xy k=(a2b2)/2/(cosFcosG)=(a2b2)/2/(cos60° cos120° )=(802602)/2/(cos60° cos120° )=(802602)/2/(0.5(0.5))=1400 5000 = x2+(1400/x)2 x1=20.707 x2=67.611 y1=1400/x1=1400/20.70767.61 y2=1400/x2=1400/67.61120.7067 u1=2 x1=2 20.707=41.414 u2=2 y1=2 67.61135.22 s=(a+b+u1)/2=(80+60+41.414)/2=90.707 S1=s (sa) (sb) (su1)=90.707 (90.70780) (90.70760) (90.70741.414)1212.455 S=2 S1=2 1212.455=2424.91



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