{"id":4053,"date":"2026-10-15T01:36:45","date_gmt":"2026-10-15T00:36:45","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/duzgun-cokgen-alani\/"},"modified":"2026-10-15T01:36:45","modified_gmt":"2026-10-15T00:36:45","slug":"duzgun-cokgen-alani","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/duzgun-cokgen-alani\/","title":{"rendered":"D\u00fczg\u00fcn \u00c7okgen Alan Hesaplay\u0131c\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">D\u00fczg\u00fcn \u00c7okgenin Alan\u0131n\u0131 Bulun<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4053\" data-favorite-title=\"D\u00fczg\u00fcn \u00e7okgen alan\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/duzgun-cokgen-alani\/\" data-favorite-excerpt=\"Herhangi bir d\u00fczg\u00fcn \u00e7okgenin alan\u0131n\u0131 kenar uzunlu\u011fu, apotem veya \u00e7evrel yar\u0131\u00e7aptan hesaplay\u0131n. Kenar say\u0131s\u0131n\u0131 ve bildi\u011finiz tek bir boyutu girin; alan, \u00e7evre ve a\u00e7\u0131lar\u0131 an\u0131nda g\u00f6r\u00fcn.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/duzgun-cokgen-alani\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4053\" data-post=\"4053\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Kenar say\u0131s\u0131 (n)<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"kenar_says_n\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"6\" min=\"3\" max=\"10000\" value=\"6\"\/><small id=\"calc-info-1\">E\u015fit kenarlar\u0131n say\u0131s\u0131; 3 veya daha fazla bir tam say\u0131 olmal\u0131d\u0131r.<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Bilinen b\u00fcy\u00fckl\u00fck<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"bilinen_byklk\"><option value=\"side\" selected>Kenar uzunlu\u011fu (s)<\/option><option value=\"apothem\">Apotem (a)<\/option><option value=\"circumradius\">\u00c7evrel yar\u0131\u00e7ap (R)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Kenar uzunlu\u011fu (s)<\/label><div class=\"term\">s<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"kenar_uzunluu_s\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"birim\" aria-label=\"Birim\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">\u00c7okgenin bir kenar\u0131n\u0131n uzunlu\u011fu.<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-5\">Apotem (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"apotem_a\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"8.66\" min=\"0\" value=\"8.66\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"birim\" aria-label=\"Birim\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Merkezin bir kenar\u0131n orta noktas\u0131na uzakl\u0131\u011f\u0131 (i\u00e7 yar\u0131\u00e7ap).<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-7\">\u00c7evrel yar\u0131\u00e7ap (R)<\/label><div class=\"term\">R<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"evrel_yarap_r\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"birim\" aria-label=\"Birim\"><option value=\"m\">m<\/option><option value=\"cm\" selected>cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-7\">Merkezin bir k\u00f6\u015feye uzakl\u0131\u011f\u0131 (\u00e7evrel \u00e7emberin yar\u0131\u00e7ap\u0131).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4053\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> \u00c7okgeniniz<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Alan<\/span><span class=\"result-term\">A<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>\u00c7evre<\/span><span class=\"result-term\">P<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Kenar uzunlu\u011fu<\/span><span class=\"result-term\">s<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Apotem<\/span><span class=\"result-term\">a<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>\u00c7evrel yar\u0131\u00e7ap<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>\u0130\u00e7 a\u00e7\u0131<\/span><span class=\"result-term\">\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-7\"><span class=\"field-title\"><span>Hesaplama ad\u0131mlar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4053\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>D\u00fczg\u00fcn \u00e7okgenin alan\u0131<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ A = \\frac{n\\,s^2}{4\\tan(\\pi\/n)} = \\frac{1}{2}\\,P\\,a = \\frac{1}{2}\\,n\\,R^2\\sin\\!\\left(\\frac{2\\pi}{n}\\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 kenar say\u0131s\u0131 (\\(n \\ge 3\\))<\/li>\n<li>\\(s\\) \u2014 bir kenar\u0131n uzunlu\u011fu<\/li>\n<li>\\(a\\) \u2014 apotem (merkezden bir kenar\u0131n orta noktas\u0131na olan uzakl\u0131k, yani i\u00e7 te\u011fet \u00e7ember yar\u0131\u00e7ap\u0131)<\/li>\n<li>\\(R\\) \u2014 \u00e7evrel yar\u0131\u00e7ap (merkezden bir k\u00f6\u015feye olan uzakl\u0131k)<\/li>\n<li>\\(P = n \\cdot s\\) \u2014 \u00e7evre<\/li>\n<li>\\(\\pi \\approx 3.14159\\)<\/li>\n<\/ul>\n<p>\u00dc\u00e7 ifade de ayn\u0131 alan\u0131 verir; hangisini biliyorsan\u0131z o boyuta uyan\u0131 kullan\u0131rs\u0131n\u0131z. Ortadaki \\(A = \\tfrac{1}{2}Pa\\) bi\u00e7imi, \u00e7okgenin \\(n\\) e\u015f \u00fc\u00e7gene b\u00f6l\u00fcnmesiyle elde edilen klasik sonu\u00e7tur; her \u00fc\u00e7genin taban\u0131 \\(s\\), y\u00fcksekli\u011fi \\(a\\)d\u0131r.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>D\u00fczg\u00fcn \u00e7okgen alan\u0131 \u2013 hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> kenar uzunlu\u011fu 10 cm olan d\u00fczg\u00fcn alt\u0131gen.<\/p>\n<p>\\[ a = \\frac{s}{2\\tan(\\pi\/n)} = \\frac{10}{2\\tan(\\pi\/6)} = \\frac{10}{2 \\cdot 0.5774} \\approx 8.660 \\text{ cm} \\]<\/p>\n<p>\\[ P = n \\cdot s = 6 \\cdot 10 = 60 \\text{ cm} \\]<\/p>\n<p>\\[ A = \\tfrac{1}{2}\\,P\\,a = \\tfrac{1}{2} \\cdot 60 \\cdot 8.660 \\approx 259.81 \\text{ cm}^2 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> alan yakla\u015f\u0131k <strong>259,81 cm\u00b2<\/strong>. Hesaplay\u0131c\u0131 ayr\u0131ca \u00e7evrel yar\u0131\u00e7ap \\(R = 10\\) cm ve 120\u00b0'lik i\u00e7 a\u00e7\u0131 de\u011ferini de verir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Kenar say\u0131s\u0131n\u0131 (n)<\/strong> girin \u2014 3 (\u00fc\u00e7gen) ile 10.000 aras\u0131 herhangi bir tam say\u0131.<\/li>\n<li><strong>Bilinen b\u00fcy\u00fckl\u00fck<\/strong> a\u00e7\u0131l\u0131r listesinden elinizdeki boyutu se\u00e7in: <em>Kenar uzunlu\u011fu (s)<\/em>, <em>Apotem (a)<\/em> veya <em>\u00c7evrel yar\u0131\u00e7ap (R)<\/em>. Yaln\u0131zca ilgili giri\u015f alan\u0131 g\u00f6r\u00fcn\u00fcr kal\u0131r.<\/li>\n<li>Beliren alana de\u011feri yaz\u0131n \u2014 <strong>Kenar uzunlu\u011fu (s)<\/strong>, <strong>Apotem (a)<\/strong> veya <strong>\u00c7evrel yar\u0131\u00e7ap (R)<\/strong> \u2014 ve birimini se\u00e7in (m, cm, mm, ft veya in).<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: <strong>Alan<\/strong> (se\u00e7ti\u011finiz birimin karesi cinsinden), ayr\u0131ca <strong>\u00c7evre<\/strong>, <strong>Kenar uzunlu\u011fu<\/strong>, <strong>Apotem<\/strong>, <strong>\u00c7evrel yar\u0131\u00e7ap<\/strong>, <strong>\u0130\u00e7 a\u00e7\u0131<\/strong> ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fcm.<\/li>\n<\/ol>\n<h2>D\u00fczg\u00fcn \u00e7okgen nedir?<\/h2>\n<p>D\u00fczg\u00fcn \u00e7okgen, b\u00fct\u00fcn kenarlar\u0131 e\u015fit uzunlukta ve b\u00fct\u00fcn i\u00e7 a\u00e7\u0131lar\u0131 e\u015fit olan, kenarlar\u0131 do\u011fru par\u00e7as\u0131ndan olu\u015fan kapal\u0131 bir \u015fekildir. Bilinen \u00f6rnekler e\u015fkenar \u00fc\u00e7gen (\\(n=3\\)), kare (\\(n=4\\)), d\u00fczg\u00fcn be\u015fgen (\\(n=5\\)) ve d\u00fczg\u00fcn alt\u0131gendir (\\(n=6\\)). B\u00fct\u00fcn kenarlar ve a\u00e7\u0131lar e\u015fit oldu\u011fundan, d\u00fczg\u00fcn bir \u00e7okgeni yaln\u0131zca iki say\u0131 tam olarak belirler: kenar say\u0131s\u0131 ve tek bir do\u011frusal boyut.<\/p>\n<p>Alan form\u00fcl\u00fc, \u00e7okgeni merkezde birle\u015fen \\(n\\) e\u015f \u00fc\u00e7gene b\u00f6lmeye dayan\u0131r. Her \u00fc\u00e7genin taban\u0131 \\(s\\) (\u00e7okgenin bir kenar\u0131) ve y\u00fcksekli\u011fi \\(a\\) (apotem) oldu\u011fundan alan\u0131 \\(\\tfrac{1}{2}sa\\)d\u0131r. \\(n\\) kenarla \u00e7arp\u0131nca \\(A = \\tfrac{1}{2}na s = \\tfrac{1}{2}Pa\\) elde edilir. Bir dairenin alan\u0131n\u0131 bulmada kullan\u0131lan mant\u0131k da ayn\u0131d\u0131r: \\(n\\) \u00e7ok b\u00fcy\u00fcd\u00fc\u011f\u00fcnde \u00e7okgen, yar\u0131\u00e7ap\u0131 \\(R\\) olan bir daireden ay\u0131rt edilemez h\u00e2le gelir ve form\u00fcl \\(\\pi R^2\\) de\u011ferine yakla\u015f\u0131r.<\/p>\n<p>Anla\u015f\u0131lmas\u0131nda fayda olan iki t\u00fcretilmi\u015f boyut vard\u0131r. <strong>Apotem<\/strong>, \u00e7okgenin i\u00e7ine s\u0131\u011fan en b\u00fcy\u00fck \u00e7emberin \u2014 her kenara orta noktas\u0131ndan de\u011fen \u00e7emberin \u2014 yar\u0131\u00e7ap\u0131d\u0131r. <strong>\u00c7evrel yar\u0131\u00e7ap<\/strong> ise b\u00fct\u00fcn k\u00f6\u015felerden ge\u00e7en \u00e7evrel \u00e7emberin yar\u0131\u00e7ap\u0131d\u0131r. Bu \u00fc\u00e7 boyut, \\(s = 2a\\tan(\\pi\/n) = 2R\\sin(\\pi\/n)\\) ve \\(a = R\\cos(\\pi\/n)\\) \u00f6zde\u015flikleriyle birbirine ba\u011fl\u0131d\u0131r; hesaplay\u0131c\u0131n\u0131n herhangi birinden di\u011ferlerini t\u00fcretebilmesinin nedeni budur.<\/p>\n<p>Sonu\u00e7larda g\u00f6sterilen <strong>i\u00e7 a\u00e7\u0131<\/strong>, \\(\\alpha = (n-2) \\cdot 180\u00b0\/n\\) form\u00fcl\u00fcnden gelir. \u0130n\u015faatta, d\u00f6\u015femecilikte ve marangozlukta i\u015fe yarar: \u00f6rne\u011fin alt\u0131genin k\u00f6\u015feleri 120\u00b0'dir; tahtalar\u0131 birle\u015ftirmek i\u00e7in 60\u00b0'lik makas kesimi yapars\u0131n\u0131z.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca d\u00fczg\u00fcn \u00e7okgenler.<\/strong> Form\u00fcller b\u00fct\u00fcn kenarlar\u0131n ve a\u00e7\u0131lar\u0131n e\u015fit olmas\u0131na dayan\u0131r. D\u00fczg\u00fcn olmayan bir \u00e7okgende \u015fekli \u00fc\u00e7gen veya yamuklara b\u00f6l\u00fcp alanlar\u0131 toplay\u0131n.<\/li>\n<li><strong>Birimler tutarl\u0131 olmal\u0131.<\/strong> Birim listesi girdiyi otomatik d\u00f6n\u00fc\u015ft\u00fcr\u00fcr ve alan kar\u015f\u0131l\u0131k gelen kare birimde verilir (\u00f6r. cm \u2192 cm\u00b2). Elle hesapl\u0131yorsan\u0131z form\u00fcl\u00fc uygulamadan \u00f6nce b\u00fct\u00fcn uzunluklar\u0131 ayn\u0131 birime getirin.<\/li>\n<li><strong>Ger\u00e7ekte \u00f6l\u00e7t\u00fc\u011f\u00fcn\u00fcz boyutu se\u00e7in.<\/strong> Uygulamada \u00e7o\u011fu zaman kenar uzunlu\u011fu de\u011fil, kar\u015f\u0131l\u0131kl\u0131 y\u00fczler aras\u0131 mesafe (\u00e7ift \\(n\\) i\u00e7in apotemin iki kat\u0131) ya da c\u0131vata dairesi yar\u0131\u00e7ap\u0131 (\u00e7evrel yar\u0131\u00e7ap) bilinir; ara bir d\u00f6n\u00fc\u015f\u00fcmden do\u011facak yuvarlama hatalar\u0131n\u0131 \u00f6nlemek i\u00e7in bu se\u00e7ene\u011fi kullan\u0131n.<\/li>\n<li><strong>B\u00fcy\u00fck \\(n\\).<\/strong> 10.000'e kadar de\u011ferler kabul edilir; bu kadar \u00e7ok kenarl\u0131 \u015fekillerde sonu\u00e7 fiilen yar\u0131\u00e7ap\u0131 \\(R\\) olan dairenin alan\u0131d\u0131r, \u00e7\u00fcnk\u00fc \\(n \\to \\infty\\) iken \\(A \\to \\pi R^2\\).<\/li>\n<li><strong>Yuvarlama.<\/strong> Sonu\u00e7lar \u00fc\u00e7 ondal\u0131k basamakla g\u00f6sterilir. \u00c7\u00f6z\u00fcm ad\u0131mlar\u0131ndaki ara de\u011ferler g\u00f6r\u00fcnt\u00fclenmek \u00fczere yuvarland\u0131\u011f\u0131ndan, elle yapaca\u011f\u0131n\u0131z kontrol son basamakta farkl\u0131l\u0131k g\u00f6sterebilir.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Herhangi bir d\u00fczg\u00fcn \u00e7okgenin alan\u0131n\u0131 kenar uzunlu\u011fu, apotem veya \u00e7evrel yar\u0131\u00e7aptan hesaplay\u0131n. Kenar say\u0131s\u0131n\u0131 ve bildi\u011finiz tek bir boyutu girin; alan, \u00e7evre ve a\u00e7\u0131lar\u0131 an\u0131nda g\u00f6r\u00fcn.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[42],"class_list":["post-4053","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-geometri"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4053","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4053"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4053\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4053"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4053"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}