a)
ducem BM inaltimea pe DC
MC=(37-7)/2=15 cm
aplicam Pitagora in triunghiul BMC
BM=√(25²-15²)=√(625-225)=√400=20 cm
A=(B+b)×h/2=(37+7)×20/2=440 cm²
b)
BC=AD=6 cm
AC=8 cm
ducem DN inaltimea pe AB
ducem CM inaltimea pe AB
notam AN=MB=x
DC=NM=10
aplicam Pitagora in triunghiul ACM
AM=10-x
CM²=8²-(10-x)²
aplicam Pitagora in triunghiul AND
DN²=6²-x²
egalam cele 2 relatii
8²-(10-x)²=6²-x²
64-100+20x-x²=36-x²
64-100+20x=36
20x=72
x=3,6
DC=10-3,6×2=2,8
DN=√(6²-3,6²)=√(36-12,96)=√23,04=4,8 cm
A=(B+b)×h/2=(10+2,8)×4,8/2=12,8×2,4=30,72 cm²
