Question

Se da trapezul ABCD cu AD//CD,m(unghiuluiA)=90°,m(unghiuluiD)=30°,AB=4cm,BC=4 radical din 3cm. Determinati aria trapezului.

Answer 1

Inaltimea CT=4cm
In triunghiul CTD: D=30 grade deci CD=CT*2=8cm
cosD=$\frac{\sqrt{3}}{2}$
TD/8=$\frac{\sqrt{3}}{2}$ deci TD=4√3cm
AD=4√3+4√3=8√3cm
$A= \frac{(AD+BC)*AB}{2}= \frac{(8\sqrt{3}+4\sqrt{3})*4}{2} \\ A=2*12\sqrt{3}=24\sqrt{3}~cm^2$