Question

Fie trapezul dreptunghic VAST,m(<VAS)=90grade,AS||VT,m(<AST)=60grade,VA=5cm,VT=3cm.Aflati perimetrul si aria trapezului

Answer 1

Fie R∈AS a.i. TR _|_ AS => VTRA-dreptunghi => VT=AR=3cm si VA=TR=5cm.

m(<TRS)=90* si m(<TSR)=60* => m(<RTS)=30*.

tg(<TSR)=tg60*=$\sqrt{3}$=$\frac{TR}{RS} =>RS= \frac{TR}{ \sqrt{3} }= \frac{5}{ \sqrt{3} } = \frac{ 5\sqrt{3} }{3} (cm).$

AS=AR+RS=$3+ 5\sqrt{3}(cm).$

$A_{VAST}= \frac{(VT+AS)*VA}{2}= \frac{6+ 5\sqrt{3} }{2}( cm^{2} ) .$