Question

Afla aria triunghiului ABC dacă :
AB=6 m ; AC = 9m ; BC =11m

Answer 1

$p = \frac{a + b + c}{2} = \frac{6 + 9 + 11}{2} = \frac{15 + 11}{2} = \frac{26}{2} = 13$

$A = \sqrt{p(p - a)(p - b)(p - c)} = \sqrt{13(13 - 6)(13 - 9)(13 - 11)} = \sqrt{13 \times 7 \times 4 \times 2} = \sqrt{91 \times 4 \times 2} = \sqrt{364 \times 2} = \sqrt{728} = 2 \sqrt{182} \: \: {m}^{2} \\ \\ \sqrt{728} = \sqrt{2 \times 2 \times 2 \times 7 \times 13} = \sqrt{(2 \times 2) \times 2 \times 7 \times 13} = \sqrt{ {2}^{2} \times 2 \times 7 \times 13 } = 2 \sqrt{2 \times 7 \times 13} = 2 \sqrt{182}$

Answer 2

Răspuns:

heron ; A =√p(p-a)(p-b)(p-c) ; p semiperimetrul ; p= (11+9+6)/2=13 ;                                     A =√13(13-11)(13-9)(13-6)=√13×2×4×7=2√182

Explicație pas cu pas: