Question

calculate
a) aria paralelogramului abcd,stiind ca AB=8 cm,BC=5√3 cm si m unghiului ABC=60 grade
b)aria dreptunghiului ABCD,stiind ca AΔBOC=13 cm²,unde ACintersectat BD={O}
c)aria rombului ABCD,stiind ca BD+16 cm si m unghi BAD=60 grade

Answer 1

$a)~A_{ABCD}=2 \cdot A_{ABC}=2 \cdot \frac{AB \cdot BC \cdot sin( \angle ABC)}{2}=AB \cdot BC \cdot sin(60\textdegree) = \\ \\ =8 \cdot 5 \sqrt{3} \cdot \frac{\sqrt{3}}{2}=60~(cm^2).$

$b)~A_{ABCD}= 4 \cdot A_{BOC}=4 \cdot 13 =52 ~(cm^2). \\ \\ c)~m( \angle BAD)=60 \textdegree ~si~AB=AD \Rightarrow \Delta ABD-echilateral \Rightarrow \\ \Rightarrow AB=AD=BD=16~cm. \\ \\ A_{ABCD}= 2 \cdot A_{ABD}=2 \cdot \frac{AB^2 \sqrt{3}}{4}= \frac{16^2 \sqrt{3}}{2}= 128~ \sqrt{3}~(cm^2).$