Question

1. Daca ABCD este trapez isoscel , AD=25 AC=26 DC=17 aflati linia mijlocie si aria.
2. Daca ABCD este trapez dreptunghic, BD=15 BC=8 DC=17 aflati aria stiind ca masura lui A=90 de grade.
3. ABC triunghi obtuzunghic cu masura lui A=105 grade AC=8 si masura lui B=30 de grade aflati perimetrul.

Answer 1

1.consideram AB II DC
AD=25
AC=26
DC=17
ducem AE_I_DC
AE²=AD²-DE²=25²-DE²=625-DE²
AE²=AC²-EC²=26²-(DC-DE)²=676-(17-DE)²=676-289+34DE-DE²=387+34DE-DE²
625-DE²=387+34DE-DE²
625=387+34DE
34DE=238
DE=238/34=7
AE=√(625-7²)=√(625-49)=√576=24
AB=17-2x7=3
linia mijlocie=(AB+DC)/2=(3+17)/2=10
A=Bxh/2=17x24/2=204