query: How to arrive to this formula $A=\sqrt{s(s-a)(s-b)(s-c)}?$
positive_passages.docid: 21745
positive_passages.text: Proof of Heron's Formula for the area of a triangle
negative_passages.docid: 30307
negative_passages.text: Find the value of $k$ in $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \ge \sqrt{a}+\sqrt{b}+\sqrt{c}+k$
negative_passages.docid: 113628
negative_passages.text: Where M is a matrix calculate a formula for M^n
negative_passages.docid: 77279
negative_passages.text: find the formula of trinomial expansion
negative_passages.docid: 33105
negative_passages.text: Find the value of $a^2-b^2+c^2$
negative_passages.docid: 20055
negative_passages.text: Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
negative_passages.docid: 115719
negative_passages.text: Find the possible values of |A + B + C |
negative_passages.docid: 65297
negative_passages.text: Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.
negative_passages.docid: 152802
negative_passages.text: How find series $\sum_{n=1}^{\infty}\frac{(-1)^{[\sqrt[m]{n}]}}{n^a}$?
negative_passages.docid: 129860
negative_passages.text: Find a formula for this sequence (and prove it).
negative_passages.docid: 109133
negative_passages.text: $a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$
negative_passages.docid: 136868
negative_passages.text: Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
negative_passages.docid: 148744
negative_passages.text: Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
negative_passages.docid: 114506
negative_passages.text: Expansion of $(1+\sqrt{2})^n$
negative_passages.docid: 73029
negative_passages.text: If a,b,c are sides of a triangle, prove: $ \sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \le \sqrt{a} + \sqrt{b} + \sqrt{c} $
negative_passages.docid: 33633
negative_passages.text: Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
negative_passages.docid: 128091
negative_passages.text: Find the range of possible values of $\sqrt{a^2+a+1}-\sqrt{a^2-a+1}$