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• Heron's Formula
  '''Heron's Formula''' (sometimes called Hero's formula) is a [[mathematical formula * [http://www.scriptspedia.org/Heron%27s_Formula Heron's formula implementations in C++, Java and PHP]
  4 KB (675 words) - 00:05, 22 January 2024
• Heron's formula
  #REDIRECT [[Heron's Formula]]
  29 bytes (3 words) - 13:55, 22 December 2007

Page text matches

• Heron's Formula
  '''Heron's Formula''' (sometimes called Hero's formula) is a [[mathematical formula * [http://www.scriptspedia.org/Heron%27s_Formula Heron's formula implementations in C++, Java and PHP]
  4 KB (675 words) - 00:05, 22 January 2024
• Brahmagupta's Formula
  Brahmagupta's formula reduces to [[Heron's formula]] by setting the side length <math>{d}=0</math>.
  3 KB (465 words) - 18:31, 3 July 2023
• Triangle
  ...s(s-a)(s-b)(s-c)}</math>, where <math>s</math> is the [[semiperimeter]] ([[Heron's Formula]]).
  4 KB (628 words) - 17:17, 17 May 2018
• Semiperimeter
  Two other well-known examples of formulas involving the semiperimeter are [[Heron's formula]] and [[Brahmagupta's formula]].
  641 bytes (97 words) - 00:28, 31 December 2020
• Area
  * [[Heron's formula]]: <math>K=\sqrt{s(s-a)(s-b)(s-c)}</math>, where <math>a, b</math === Other formulas <math>K = f(a,b,c)</math> equivalent to Heron's ===
  6 KB (1,181 words) - 22:37, 22 January 2023
• Trigonometry
  ...thagorean Theorem]] and is used to prove several famous results, such as [[Heron's Formula]] and [[Stewart's Theorem]]. However, it sees limited applicabili
  8 KB (1,217 words) - 20:15, 7 September 2023
• 2005 AIME I Problems/Problem 15
  ...ath>m = 4\sqrt{2}</math>, and thus <math>AB = 26</math>. You can now use [[Heron's Formula]] to finish. The answer is <math>24 \sqrt{14}</math>, or <math>\b Finally, you can use [[Heron's Formula]] to get that the area is <math>24\sqrt{14}</math>, giving an ans
  5 KB (906 words) - 23:15, 6 January 2024
• 2005 AIME II Problems/Problem 14
  From here, we can use Heron's Formula to find the altitude. The area of the triangle is <math>\sqrt{21*
  13 KB (2,129 words) - 18:56, 1 January 2024
• 1985 AIME Problems/Problem 9
  This triangle has [[semiperimeter]] <math>\frac{2 + 3 + 4}{2}</math> so by [[Heron's formula]] it has [[area]] <math>K = \sqrt{\frac92 \cdot \frac52 \cdot \fr
  5 KB (763 words) - 16:20, 28 September 2019
• 1986 AIME Problems/Problem 2
  ...th side-lengths <math>2\sqrt5,2\sqrt6,</math> and <math>2\sqrt7,</math> by Heron's Formula, the area is the square root of the original expression.
  3 KB (460 words) - 00:44, 5 February 2022
• 1989 AIME Problems/Problem 15
  === Solution 2 (Mass Points, Stewart's Theorem, Heron's Formula) === ...se and the <math>h_{\triangle ABC} = 2h_{\triangle BCP}</math>. Applying [[Heron's formula]] on triangle <math>BCP</math> with sides <math>15</math>, <math>
  13 KB (2,091 words) - 00:20, 26 October 2023
• 1992 AIME Problems/Problem 13
  ...>, so the area is <math>\frac14\sqrt {(81^2 - 81x^2)(81x^2 - 1)}</math> by Heron's formula. By AM-GM, <math>\sqrt {(81^2 - 81x^2)(81x^2 - 1)}\le\frac {81^2 ...e after letting the two sides equal <math>40x</math> and <math>41x</math>. Heron's gives
  4 KB (703 words) - 02:40, 29 December 2023
• 1995 AIME Problems/Problem 14
  ...minor arc <math>\stackrel{\frown}{BC}</math>. The former can be found by [[Heron's formula]] to be <math>[BCE] = \sqrt{60(60-48)(60-42)(60-30)} = 360\sqrt{3
  3 KB (484 words) - 13:11, 14 January 2023
• 1999 AIME Problems/Problem 15
  Now see that by Heron's, <cmath>[DEP] = [DEF] = \sqrt{(16 + 2 \sqrt{13})(16 - 2 \sqrt{13})(1 + 2
  7 KB (1,107 words) - 20:34, 27 January 2023
• 1999 AIME Problems/Problem 14
  ...th>[CAP] + [ABP] + [BCP] = [ABC] = \sqrt {(21)(8)(7)(6)} = 84</math>, by [[Heron's formula]].
  7 KB (1,184 words) - 13:25, 22 December 2022
• 1999 AIME Problems/Problem 12
  ...x \cdot 2}{2} = 50 + x</math>, we get <math>(21)(50 + x) = A</math>. By [[Heron's formula]], <math>A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{(50+x)(x)(23)(27)}</
  3 KB (472 words) - 15:59, 25 February 2022
• 2001 AIME I Problems/Problem 12
  ...</math> and <math>\sqrt{4^{2}+6^{2}}</math>, so using the expanded form of heron's formula, <cmath>\begin{align*}[ABC]&=\sqrt{\dfrac{2(a^{2}b^{2}+b^{2}c^{2}
  6 KB (1,050 words) - 18:44, 27 September 2023
• 2001 AIME I Problems/Problem 7
  ...ABC</math> is <math>s = \frac{20 + 21 + 22}{2} = \frac{63}{2}</math>. By [[Heron's formula]], the area of the whole triangle is <math>A = \sqrt{s(s-a)(s-b)(
  9 KB (1,540 words) - 08:31, 1 December 2022
• 2002 AIME I Problems/Problem 13
  ...asy to get that <math>\sin \angle AEP = \frac{\sqrt{55}}{8}</math> (equate Heron's and <math>\frac{1}{2}ab\sin C</math> to find this). Now note that <math>\ \end{matrix}\right|=\frac{16}{81}.</cmath>By Heron's Formula, we have <math>[ABC]=\frac{81\sqrt{55}}{2}</math> which immediate
  6 KB (974 words) - 13:01, 29 September 2023
• 2002 AIME I Problems/Problem 10
  ...Now we have all segments of triangles AGF and ADC. Joy! It's time for some Heron's Formula. This gives area 10.95 for triangle AGF and 158.68 for triangle A
  4 KB (643 words) - 22:44, 8 August 2023

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