Question

Fie ABCD un trape isosvel, la care se stiu AB|| CD , AB=24 cm CD=12 cm si m (<B )= 46°.Aflati aria trapezului si aria triunchiului ADC

Answer 1

Am,desenat,trapezul,cu,baza,mare,AB,jos
Coboram,perpendiculara,din,C,pe,AB,si,o,notam,cu,E,si,din,D,si,o,notam,cu,F
Avem,tr.dr.CEB
Avem,m(CBE)=45=>m(BCE)=45=>tr.dr.isoscel
EB=AF=(AB-CD)/2=(24-12)/2=12/2=6
cos45=cateta,alaturata/ipotenuza
radical.din.2/2=6/BC=>BC=2x6/rad.din.2
BC=12rad.din.2/2=>BC=6rad.din.2
CE,este,si,inaltimea,in,trapez
O,aflam,din,tr.dr.isoscel,CEB,cu,t.Pit
CEpatrat+EBpatrat=BCpatrat
CEpatrat=BCpatrat-EBpatrat
CEpatrat=72-36
CEpatrat=36=>CE=6
Aria=(B+b)xCE/2=(24+12)x6/2
Aria=36x3=108cmpatrati