Question

Cum aflu aria unui trapez dreptunghic stiind ca bazele au 8 radical din 3 si 18 radical din 3 si ca diagonalele sunt perpendiculare intre ele? Dau funda.

Answer 1

   
$\text{Un trapez care are diagonalele perpendiculare, } \\ \text{are inaltimea egala cu linua mijlocie.} \\ \\ A_{trapez} = \frac{B+b}{2}\times h~~~~~~unde: \\ \\ \frac{B+b}{2} = linia~mijlocie~a ~trapezului. \\ \\ h = inaltimea = \text{linia mijlocie, deoarece are diagonalele perpendiculare} \\ \\ =\ \textgreater \ ~~~~h = \frac{B+b}{2} \\ \\ =\ \textgreater \ \;\;\;A_{trapez} = \frac{B+b}{2}\times h=\frac{B+b}{2}\times \frac{B+b}{2}=\left(\frac{B+b}{2} \right)^2 =$

$=\left(\frac{18 \sqrt{3} +8\sqrt{3} }{2} \right)^2 =\left(\frac{26 \sqrt{3} }{2} \right)^2=(13 \sqrt{3})^2=169\times 3 = \boxed{507\;cm^2}$