Ratio in trapezium

The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid

Correct result:

o =  106.9691 cm

Solution:

v:a:c=1:6:3 S=324 cm2 β=35   a=6v c=3v  S=a+c2 v S=6v+3v2 v S=92 v2  v=2 S/9=2 324/9=6 2 cm8.4853 cm a=6 v=6 8.4853=36 2 cm50.9117 cm c=3 v=3 8.4853=18 2 cm25.4558 cm  a=x1+c+x2 tanβ=v:x2  x2=v/tanβ=v/tan35 =8.4853/tan35 =8.4853/0.700208=12.11824 cm  x1=acx2=50.911725.455812.118213.3376 cm  b=v2+x22=8.48532+12.1182214.7936 cm d=v2+x12=8.48532+13.3376215.808 cm  o=a+b+c+d=50.9117+14.7936+25.4558+15.808106.9691=106.9691 cm   Verifying Solution:  S1=a+c2 v=50.9117+25.45582 8.4853=324 cm2



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