Question

Fie trapezul dreptunghic ABCD cu AB//CD  ,m (<A)=90 grade , AB=20 cm , DC=8cm  si AD=9 cm 
a) Aflati perimetrul si aria trapezului ABCD
b) Aflati distanta  de la A la latura BC.
c) Daca AD reunit cu BC={E} , calculati aria triunghiului AEB

Answer 1

a) fie CM_|_AB =>CM=AD=9
BM=AB-CD=20-8=12
In ΔCMB
CB²=BM²+CM²=12²+9²=144+81=225
CD=15
Perimetru trapez=AB+BC+CD+AD=10+15+8+9=52 cm
Aria trapez= (AB+DC)*AD:2= 126 cm²

b) Notam AN distanta de la A la latura BC=> AN_|_BC
in ΔABC avem:
CM*AB=AN*CB
9*20=AN*15
AN=9*20:15
AN=12

c)in ΔEAB
ED/EA=CD/AB
ED/(ED+AD)=8/20
ED/(ED+9)=2/5
5*ED=2*ED+18
3*ED=18
ED=6
EA=AD+ED=6+9=15
Aria ΔEAB=EA*AB:2=15*20:2=150 cm²