The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.

Correct result:

o =  22.2229 cm
S =  19.0681 cm2

Solution:

a=10 cm c=6 cm α=50  x=(ac)/2=(106)/2=2 cm  cosα=x:r  r=x/cos(α)=2/cos(50)=3.11145 cm  o=a+c+2 r=10+6+2 3.1114=22.2229 cm
tanα=h:x  h=x tan(α)=2 tan(50)=2.38351 cm  S=a+c2 h=10+62 2.3835=19.0681 cm2



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