Question

Se da trapezul ABCD cu AD||CB, masura unghiuluii A= 90 grade, masura unhiului D =30 grade, AB=4cm, BC= 4√3cm. Cat este aria trapezului?

Answer 1

Ducem CE_|_AD
In ΔCDE, <CDE=30°=> putem afla DE prin 2 metode:
1. tg  <CDE=CE/DE=> √3/3=4/DE=> DE=4√3
2. CE=CD/2=> AB=CE=> CD=8=> DE²=CD²-CE²=64-16=48=>DE=4√3

=>AD=DE+EA=DE+CB=4√3+4√3=8√3
Aria ABCD=(AD+CB)*AB/2=(8√3+4√3)*4/2=12√3*2=24√3