Question

Rombul abcd si patratul efgh au perimetrele egale. Stiind ca Aabcd=1/2 Aefgh determinati masurile unghiurile rombului abcd

Answer 1

rombul ABCD are laturile congruente, Pr=4a
patratul EFGH are laturile congruente, Pp=4b
 Pr=Pp ⇒ 4a=4b ⇒ a=b
aria romb cu sinus:
Ar=a^2 sin(B)=Ap/2=a^2/2
sin(B)=1/2 ⇒ ∡B=30°
∡B=∡D=30°
∡A=∡C=(360 - ∡B - ∡D)/2=150°