a)ABCD -dreptungi
[AD]≡[BC]
AD=BC
[AB]≡[DC]
AB=DC=4
DB;AC-diag
[DB]≡[AC]
DB=AC=6 =>[DB-bisect <ABC
mas<ABD=mas<DBC=mas<ABC/2= 90/2=45 grade
sin<DBC= 45= √2/2
ΔBAD, mas<A=90
AD²=DB²-AB²= 6²-4²= 36-16=20 =>AD=2√5
P ABCD=2L+2l= 2*AB+2*AD= 2*4+ 2*2√5= 8+4√5
b)ΔDAB,mas<A=90
AM_|_DB
AM-h
AM=AD*AB/DB= 4√5 *4/6= 2√5 *4/3= 8√5/3
ΔAMD, mas<M=90
DM²=AD²-AM²= (4√5)² -(8√5/3)²= 80 -320/9 aducem la acelasi numitor
DM²= (720-320)/9= 400/9 =>DM=20/3
ΔADE, mas<D=90
DM_|_AE
DM²=AM*ME
(20/3)²= 8√5/3 *ME
400/9 =8√5/3 *ME
ME= (400/9)/(8√5/3)
ME=400/9 *3/8√5
ME= 50/3√5= 50√5/3*5= 10√5/3
ΔDME, mas<M=90
DE²=DM²+ME²= (20/3)² +(10√5/3)²= 400/9 + 500/9= 900/9=100 =>DE=10
