{"id":1827,"date":"2024-04-16T07:18:15","date_gmt":"2024-04-16T07:18:15","guid":{"rendered":"https:\/\/domath.surju.ee\/?page_id=1827"},"modified":"2024-12-30T19:35:43","modified_gmt":"2024-12-30T19:35:43","slug":"pyramid","status":"publish","type":"page","link":"https:\/\/domath.surju.ee\/et\/pyramiid\/","title":{"rendered":"P\u00fcramiid"},"content":{"rendered":"

P\u00fcramiid<\/strong><\/span><\/h1>\r\n\r\n

Pu\u0308ramiidiks<\/strong> <\/span>nimetatakse hulk­tahukat, mille \u00fcks tahk on hulknurk ja k\u00f5ik \u00fclej\u00e4\u00e4nud tahud on \u00fchise tipuga kolmnurgad.
\r\n
\r\n\u00dchise tipuga kolm­nurgad on pu\u0308ramiidi ku\u0308lg­tahud<\/strong>, nende kolm­nurkade u\u0308hised ku\u0308ljed on pu\u0308ramiidi ku\u0308lg­servad<\/strong>.
\r\nKu\u0308lg­tahkude u\u0308hist tippu nimetatakse pu\u0308ramiidi tipuks<\/strong>.
\r\nHulk­nurk, millel on iga kolm­nurgaga u\u0308ks u\u0308hine ku\u0308lg, on pu\u0308ramiidi p\u00f5hi­tahk<\/strong> ehk p\u00f5hi<\/strong>.
\r\nP\u00fcramiidi p\u00f5hja k\u00fclgi nimetatakse pu\u0308ramiidi p\u00f5hi­servadeks<\/strong>.
\r\nP\u00f5hiservade arvu j\u00e4rgi jagatakse p\u00fcramiidid kolmnurkseteks, nelinurkseteks, viisnurkseteks,<\/strong> ehk \u00fcldiselt n-nurkseteks.<\/strong>
\r\n
\r\nPu\u0308ramiidi k\u00f5rguseks<\/strong> nimetatakse rist­l\u00f5iku (v\u00f5i selle pikkust) pu\u0308ramiidi tipust pu\u0308ramiidi p\u00f5hjani
\r\nTipu kaugus p\u00f5hjast on p\u00fcramiidi k\u00f5rguseks H.<\/strong>
\r\nP\u00fcramiidi k\u00fclgtahu k\u00f5rgust nimetatakse apoteemiks m.
\r\n
\r\n<\/strong>Korrap\u00e4raseks p\u00fcramiidiks nimetatakse p\u00fcramiid, mille p\u00f5hitahud on korrap\u00e4rased hulknurgad (v\u00f5rdsete k\u00fclgedega hulknurgad) <\/strong>ja p\u00fcramiidi k\u00f5rguse alguspunkt asub p\u00f5hja keskpunktis.
\r\nKorrap\u00e4rase p\u00fcramiidi k\u00fclgtahud on v\u00f5rdsed v\u00f5rdhaarsed kolmnurgad, 
\r\n
\r\n<\/p>\r\n

\"\"<\/p>\r\n\r\n

Ruumala valemid<\/strong><\/span><\/h4>\r\n\r\n\r\n\r\n
\r\n
Korrap\u00e4rane nelinurkne p\u00fcramiid<\/strong><\/span><\/h5>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
\"\"\"\"<\/td>\r\n\r\n

P\u00fcramiidi ruumala v\u00f5rdub \u00fche kolmandikuga p\u00f5hja pindala ja k\u00f5rguse korrutisest. <\/p>\r\n

\"\"
\r\n   Sp <\/sub> = a2<\/sup><\/p>\r\n<\/td>\r\n

\r\n

P\u00f5hjaks on ruut <\/strong>
\r\na – p\u00f5hiserv, p\u00f5hja k\u00fclg, ruudu k\u00fclg<\/strong><\/p>\r\n

H –  p\u00fcramiidi k\u00f5rgus<\/strong><\/p>\r\n

Sp<\/sub> – p\u00f5hja pindala<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
\r\n
 Kolmnurkne p\u00fcramiid<\/strong><\/span><\/h5>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
\"\"<\/td>\r\n\"\"
\r\n
\r\n\"\"<\/td>\r\n		\r\n
H –  p\u00fcramiidi k\u00f5rgus<\/h6>\r\n
Sp<\/sub> <\/strong> – p\u00f5hja
\r\npindala<\/h6>\r\n
a – p\u00f5hiserv
\r\nh- p\u00f5hja k\u00f5rgus<\/h6>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n
\r\n

T\u00e4ispindala valemid<\/strong><\/span><\/h4>\r\n\r\n\r\n\r\n
\r\n
Korrap\u00e4rane nelinurkne p\u00fcramiid<\/strong><\/span><\/h5>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
\"\"\"\"<\/strong>\r\n

\"\"\"\"<\/strong><\/p>\r\n<\/td>\r\n

\r\n

St <\/sub>= Sk<\/sub> +  Sp<\/sub><\/strong><\/p>\r\n

P = 4a<\/strong><\/p>\r\n

\"\"<\/p>\r\n

Sk <\/sub>= 1\/2 x 4a x m =2am<\/strong><\/p>\r\n

Sp<\/sub> = a2<\/sup><\/strong><\/p>\r\n

P\u00fcramiidi k\u00fclgpindala (Sk <\/sub>) = p\u00fcramiidi k\u00fclgtahtkude pindalade summa<\/strong><\/b><\/p>\r\n<\/td>\r\n

\r\n
St <\/sub><\/strong> – t\u00e4ispindala<\/h6>\r\n

Sk<\/sub> <\/strong> -k\u00fclgpindala<\/p>\r\n

Sp<\/sub><\/strong> – p\u00f5hja pindala<\/p>\r\n

a -p\u00f5hiserv, ruudu k\u00fclg <\/h6>\r\n
H –  p\u00fcramiidi k\u00f5rgus<\/h6>\r\n

P –  P\u00f5hja \u00fcmberm\u00f5\u00f5t<\/p>\r\n

l =m – p\u00fcramiidi apoteem,  k\u00fclgrahu k\u00f5rgus, <\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
\r\n
Kolmnurkne p\u00fcramiid<\/strong><\/span><\/h5>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
\"\"<\/td>\r\n\r\n

St <\/sub>= Sk<\/sub> +  Sp<\/sub><\/strong><\/p>\r\n

\"\"
\r\nP = a+ b+ c (erik\u00fclgse kolmnurga korral)
\r\nP = 3a (v\u00f5rdk\u00fclgse kolmnurga korral)<\/p>\r\n

P\u00f5hja pindala  =  kolmnurga pindala
\r\n\"\"
\r\n
\r\n
\r\n<\/strong><\/p>\r\n

P\u00fcramiidi k\u00fclgpindala (Sk <\/sub>) = p\u00fcramiidi k\u00fclgtahtkude (kolmnurkade) pindalade summa<\/strong><\/b><\/p>\r\n<\/td>\r\n

\r\n
St <\/sub><\/strong> – t\u00e4ispindala<\/h6>\r\n

Sk<\/sub> <\/strong> -k\u00fclgpindala<\/p>\r\n

Sp<\/sub><\/strong> – p\u00f5hja pindala<\/p>\r\n

P –  p\u00f5hja \u00fcmberm\u00f5\u00f5t<\/p>\r\n

H –  p\u00fcramiidi k\u00f5rgus<\/h6>\r\n
a, b, c -p\u00f5hiservad (p\u00f5hjaks oleva kolmnurga k\u00fcljed)<\/h6>\r\n

l =m – p\u00fcramiidi apoteem,  k\u00fclgrahu k\u00f5rgus, .<\/p>\r\n

P\u00f5hja pindala  = p\u00f5hitahu pindala<\/strong><\/p>\r\n

h – p\u00f5hja k\u00f5rgus<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

 <\/p>","protected":false},"excerpt":{"rendered":"

P\u00fcramiid Pu\u0308ramiidiks nimetatakse hulk­tahukat, mille \u00fcks tahk on hulknurk ja k\u00f5ik \u00fclej\u00e4\u00e4nud tahud on \u00fchise tipuga kolmnurgad. \u00dchise tipuga kolm­nurgad on pu\u0308ramiidi ku\u0308lg­tahud, nende kolm­nurkade u\u0308hised ku\u0308ljed on pu\u0308ramiidi ku\u0308lg­servad. Ku\u0308lg­tahkude u\u0308hist tippu nimetatakse pu\u0308ramiidi tipuks. Hulk­nurk, millel on iga kolm­nurgaga u\u0308ks u\u0308hine ku\u0308lg, on pu\u0308ramiidi p\u00f5hi­tahk ehk p\u00f5hi. P\u00fcramiidi p\u00f5hja k\u00fclgi nimetatakse pu\u0308ramiidi p\u00f5hi­servadeks. […]<\/p>\n

Read More… from P\u00fcramiid<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_eb_attr":"","_uag_custom_page_level_css":"","footnotes":""},"categories":[],"tags":[58,57,63,59],"class_list":["post-1827","page","type-page","status-publish","hentry","tag-english-p","tag-estonian-p","tag-greek-pi","tag-spanish-p"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"menu-24x24":false,"menu-36x36":false,"menu-48x48":false},"uagb_author_info":{"display_name":"Yessica Caceres","author_link":"https:\/\/domath.surju.ee\/et\/author\/yessica\/"},"uagb_comment_info":0,"uagb_excerpt":"P\u00fcramiid Pu\u0308ramiidiks nimetatakse hulk­tahukat, mille \u00fcks tahk on hulknurk ja k\u00f5ik \u00fclej\u00e4\u00e4nud tahud on \u00fchise tipuga kolmnurgad. \u00dchise tipuga kolm­nurgad on pu\u0308ramiidi ku\u0308lg­tahud, nende kolm­nurkade u\u0308hised ku\u0308ljed on pu\u0308ramiidi ku\u0308lg­servad. Ku\u0308lg­tahkude u\u0308hist tippu nimetatakse pu\u0308ramiidi tipuks. Hulk­nurk, millel on iga kolm­nurgaga u\u0308ks u\u0308hine ku\u0308lg, on pu\u0308ramiidi p\u00f5hi­tahk ehk p\u00f5hi. P\u00fcramiidi p\u00f5hja k\u00fclgi nimetatakse pu\u0308ramiidi p\u00f5hi­servadeks.…","_links":{"self":[{"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/pages\/1827","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/comments?post=1827"}],"version-history":[{"count":6,"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/pages\/1827\/revisions"}],"predecessor-version":[{"id":5252,"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/pages\/1827\/revisions\/5252"}],"wp:attachment":[{"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/media?parent=1827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/categories?post=1827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/domath.surju.ee\/et\/wp-json\/wp\/v2\/tags?post=1827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}