ABCD-trapez
[AD]=[BC]=24
mas<A=mas<B=60
[AC];[BD]-diag
[AC]=[BD]
[AC] _|_ [BC] =>ΔACB -dreptunghic, mas<ACB= 90
ΔACB, mas<ACB=90
mas<ABC=60 =>mas<BAC=90 -60= 30 grade =>
=>BC=AB/2
24=AB/2 =>AB=2*24=48
AC²=AB²-BC²= 48² -24²= 2304- 576= 1728 =>AC= 2³*3 √3= 8*3√3= 24√3
b)[AC]=[DB]=24√3
a) ΔACB, mas<ACB=90
fie [CM] _|_ [AB]
[CM]-inaltime
CM=AC*BC/AB= 24√3 * 24/48= 24√3 * 1/2= 12√3
ΔBMC, mas<M=90
MB²=BC²-CM²= 24²- (12√3)²= 576- 432= 144 =>MB=12
ABCD-trapez isoscel
fie [DN] _|_ [AB]
[DN]-inaltime
[AN]=[MB]= 12
[MN]=[DC]= (AB-AM-MB)= 48 -12-12= 48-24=24
=>[DC]=24
A ABCD =(B+b)*h/2= (48+24)*12√3 /2= 72*6√3= 432√3 cm²
P ABCD= AB+BC+AD+DC= 48+24+24+24= 120 cm
