Create the page "Heron" on this wiki! See also the search results found.

Page title 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
• 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 (1,169 words) - 15:28, 13 May 2024
• 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
• 2003 AIME II Problems/Problem 6
  ...area of <math>\Delta ABC</math> either like the first solution or by using Heron’s Formula. Then, draw the medians from <math>G</math> to each of <math>A, <math>[ABC]</math> can be calculated as 84 using Heron's formula or other methods. Since a <math>180^{\circ}</math> rotation is eq
  5 KB (787 words) - 17:38, 30 July 2022
• 2000 AIME II Problems/Problem 12
  By [[Heron's Formula]] the area of <math>\triangle ABC</math> is (alternatively, a <ma
  3 KB (532 words) - 13:14, 22 August 2020
• Incircle
  *The formula above can be simplified with Heron's Formula, yielding <math>r = \sqrt{\frac{(s-a)(s-b)(s-c)}{s}}.</math> *The [[area]] of the [[triangle]] by [[Heron's Formula]] is <math>A=\sqrt{s(s-a)(s-b)(s-c)}</math>.
  2 KB (384 words) - 18:38, 9 March 2023
• Furman University Wylie Mathematics Tournament/1996 Senior Exam/Solutions
  ...of the squares is <math> 4^{2}+13^{2}+15^{2}=410. </math> Now after using Heron’s Formula, we have that the area of the triangle is 24. Thus, the total a ...) \Longrightarrow \cos{\alpha}=\frac{253}{13 \cdot 25}. </math> Now, using Heron’s Formula, we see that the area of the triangle is 204, so <math> \frac{1
  9 KB (1,364 words) - 15:59, 21 July 2006
• University of South Carolina High School Math Contest/1993 Exam/Problem 29
  One simple solution is using [[area]] formulas: by [[Heron's formula]], a [[triangle]] with sides of length 2, 3 and 4 has area <math>
  2 KB (219 words) - 09:57, 31 August 2012
• Hero's Formula
  #REDIRECT [[Heron's Formula]]
  29 bytes (3 words) - 13:27, 7 January 2008
• 2007 AIME II Problems/Problem 9
  ...we can find that <math>EF = \sqrt {63^2 + 280^2} = 287</math>. We then use Heron's formula to get:
  5 KB (818 words) - 11:05, 7 June 2022
• Mock AIME 3 Pre 2005 Problems/Problem 1
  ...triangle are <math>10</math>, <math>3+r</math>, and <math>7+r</math>. From Heron's Formula, <math>84=\sqrt{(10+r)(r)(7)(3)}</math>, or <math>84*84=r(10+r)*2
  795 bytes (129 words) - 10:22, 4 April 2012
• Mock AIME 3 Pre 2005 Problems/Problem 14
  Using Heron's formula,
  3 KB (563 words) - 02:05, 25 November 2023
• 2007 AIME II Problems/Problem 15
  First, apply [[Heron's formula]] to find that <math>[ABC] = \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = Consider a 13-14-15 triangle. <math>A=84.</math> [By Heron's Formula or by 5-12-13 and 9-12-15 right triangles.]
  11 KB (2,099 words) - 17:51, 4 January 2024
• 1961 IMO Problems/Problem 2
  By Heron's formula, we have and the RHS becomes <math>4\sqrt{3}\sqrt{(x+y+z)xyz}</math> If we use Heron's formula.
  5 KB (860 words) - 13:12, 13 February 2024
• Circumradius
  ...w the inradius, you can find the area of the triangle by [[Heron's Formula|Heron’s Formula]]: Which follows from the Heron's Formula and <math>R=\frac{abc}{4A}</math>.
  4 KB (729 words) - 16:52, 19 February 2024
• 2006 AIME II Problems/Problem 15
  ...of the triangle is <math>s = \frac{8A + 10A + 12A}{2} = 15A</math> so by [[Heron's formula]] we have <cmath>A = \sqrt{15A \cdot 7A \cdot 5A \cdot 3A} = 15A^
  4 KB (725 words) - 17:18, 27 June 2021
• 2000 AMC 12 Problems/Problem 19
  ...DE, DE</math>, to be <math>\frac{1}{2}</math> units long. We can now use [[Heron's Formula]] on <math>ABC</math>. Let's find the area of <math>\Delta ABC</math> by Heron,
  3 KB (547 words) - 17:37, 17 February 2024
• 2007 AMC 10B Problems/Problem 11
  ...1}{2}Bh = \frac {abc}{4R}</math> (or we could use <math>s = 4</math> and [[Heron's formula]]),
  5 KB (851 words) - 22:02, 26 July 2021
• 2008 AMC 12B Problems/Problem 25
  ...side of length <math>8</math> in a <math>5-7-8</math> triangle, and using Heron's, the area of such a triangle is <math>\sqrt{10(5)(3)(2)} = 10 \sqrt{3} =
  12 KB (2,015 words) - 20:54, 9 October 2022
• 2002 AMC 10A Problems/Problem 13
  By [[Heron's formula]], the area is <math>150</math>, hence the shortest altitude's le
  3 KB (395 words) - 13:22, 8 November 2021
• 2009 AIME I Problems/Problem 12
  ...Now we can compute the area of <math>\triangle ABI</math> in two ways: by heron's formula and by inradius times semiperimeter, which yields ...ath>, <math>y + z</math> and <math>x + z</math>, the square of its area by Heron's formula is <math>(x+y+z)xyz</math>.
  12 KB (1,970 words) - 22:53, 22 January 2024
• 2002 AMC 12A Problems/Problem 23
  Then by using [[Heron's Formula]] on <math>ABD</math> (with sides <math>12,7,9</math>), we have < ...= 12</math>. We now know all sides of <math> \triangle ABD</math>. Using [[Heron's Formula]] on <math>\triangle ABD</math>, <math>\sqrt{(14)(2)(7)(5)} = 14\
  6 KB (899 words) - 01:41, 5 July 2023
• 2010 AIME II Problems/Problem 12
  ...gles must be <math>s-8x,s-8x,16x</math> and <math>s-7x,s-7x,14x</math>. By Heron's Formula, we have ...l side lengths. Plugging <math>8x</math> and <math>7x</math> directly into Heron's gives <math>s=338</math>, but for this to be true, the second triangle wo
  2 KB (386 words) - 12:54, 21 November 2023
• 2010 AMC 10B Problems/Problem 7
  An alternative way to find the area of the triangle is by using Heron's formula, <math>A=\sqrt{(s)(s-a)(s-b)(s-c)}</math> where <math>s</math> is
  2 KB (318 words) - 09:00, 1 September 2022
• 2011 AIME I Problems/Problem 4
  ...find <math>r</math>, we can use the formula <math>rs = [ABC]</math> and by Heron's, <math>[ABC] = \sqrt{181 \cdot 61 \cdot 56 \cdot 64} \implies r = \sqrt{\
  6 KB (1,068 words) - 18:52, 2 August 2023
• 2011 AIME I Problems/Problem 8
  ...lue of <math>h</math> is thus <math>\frac{2K}{57},</math> and note that by Heron's formula the area of <math>\triangle ABC</math> is <math>20\sqrt{221}</mat Note that the area is given by Heron's formula and it is <math>20\sqrt{221}</math>. Let <math>h_i</math> denote
  6 KB (1,077 words) - 21:47, 12 April 2022
• 2011 AIME II Problems/Problem 10
  .../math>, <math>20</math>, and <math>24</math>, we can compute its area with Heron's formula:
  11 KB (1,720 words) - 03:12, 18 December 2023
• 1996 AHSME Problems/Problem 27
  ...math> and <math>B</math>). We can now find the area of the triangle using Heron's formula:
  7 KB (1,046 words) - 11:42, 30 September 2023
• 2011 AMC 8 Problems/Problem 16
  ==Solution 2 (Using Heron's Formula)== Using Heron's formula, we can calculate the area of the two triangles. The formula stat
  2 KB (371 words) - 16:51, 21 January 2024
• 2012 AMC 12A Problems/Problem 16
  ...triangle is <math>\frac{abc}{4A}</math> and that the area of a triangle by Heron's formula is <math>\sqrt{(S)(S-a)(S-b)(S-c)}</math> with <math>S</math> as
  9 KB (1,496 words) - 02:40, 2 October 2022
• 2012 AMC 12A Problems/Problem 18
  By Heron's formula for the area of a triangle we have that the area of triangle <mat
  4 KB (717 words) - 19:07, 28 July 2021
• Mock AIME I 2012 Problems/Problem 3
  Use Heron's formula to find <math>A=[MNO]=\frac{33}{4}\sqrt{195}</math>. Also note fr
  1 KB (208 words) - 17:31, 7 April 2012
• 2012 AMC 12B Problems/Problem 20
  By [https://en.wikipedia.org/wiki/Heron%27s_formula Heron's Formula] <math>S_1 = \sqrt{\frac{b+c+d-a}{2} \cdot \frac{c+d-a-b}{2} \cdo
  4 KB (670 words) - 07:14, 27 December 2022

View (previous 50 | next 50) (20 | 50 | 100 | 250 | 500)