Nharaunda yepasi pejeri: kubva kune zvitatu kusvika ku-polygonal

Majeri akasiyana akasiyana kubva kune mumwe. Panguva imwe chete, vane zvakawanda zvakafanana. Kuti uwane nzvimbo yegadziriro yejeri, zvichave zvakakosha kuti unzwisise rudzi rwemhando dzayo.

Nyanzvi huru

Iyo jeri iri chero polyhedron ine mitezo yechipfuva ine mufananidzo weparallelogram. Muchiitiko ichi, inogona kuva chero polyhedron - kubva padetatu kusvika kune n-gon. Uye zvigaro zvejeri zvinogara zvakaenzana. Izvo zvisingashandisi kune zviso zvakatarisana - zvinogona kusiyana zvakakura muhukuru.

Mukugadzirisa matambudziko, kwete chete nzvimbo yepasi yejeri inosangana. Zvinogona kunge zvakakosha kuzivikanwa pamusoro penzvimbo, iyo, yezviso zvose zvisiri zvigaro. Iyo yose yakakwana ichave iko kubatana kwezviso zvose zvinoumba chirongwa.

Dzimwe nguva mumabasa kune urefu. Izvo zvinongoratidzika kune zvigaro. Iyo diagonal ye polyhedron chikamu chinobatanidza miviri miviri muzviviri izvo zvisiri zvechiso chimwechete.

Inofanira kuonekwa kuti nharaunda yechitsuwa chemajeri chaiyo kana oblique hazvibvi pamakona pakati pavo uye zviso zvakatarisa. Kana vane zviyero zvakafanana mumashure ekudenga nepamusoro, ipapo nzvimbo dzavo dzichaenzana.

Triangular prism

Iyo ine mucheka chimiro chine maziso matatu, kureva, katatu. Sezvaunoziva, zvinoitika kune zvakasiyana. Kana iyo katatu yakagadzirwa nemakona mana, zvino inokwana kuyeuka kuti nzvimbo yayo inotaridzwa nehafu yezvibereko zvemakumbo.

Izwi remasvomhu rinotevera: S = ½ av.

Kuti uwane nzvimbo yechitubu chechirwere chechirwere chetatu mufomu, mazita aya anotevera achabatsira: Heron uye iyo iyo imwe hafu yechipfuva inotorwa kusvika pakakwirira yakatorwa nayo.

Muumbi wekutanga unofanira kunyorwa nenzira inotevera: S = √ (p (p-a) (p-c) (p-c)). Munhoroondo iyi pane hafu-yakakwirira (p), kureva kuti, chiyero chemativi matatu chakakamurwa kuva maviri.

Wechipiri: S = ½ n _a * a.

Kana iwe uchida kuziva nzvimbo yechitubu chechirwere chetatu, icho chakarurama, ipapo hutatu hunoenzaniswa. Kwaari, pane chirevo: S = ¼ a ² * √3.

Chirwere chekodrangular

Nheyo yaro ndeipi yeiyo inozikamwa quadrangles. Inogona kuva rectangle kana kukwereka, parallelepiped kana rhombus. Muchiitiko chimwe nechimwe, kuitira kuti tiverenge nzvimbo yezvigaro zvejeri, tinoda isu pachedu.

Kana nheyo iri rectangle, ipapo nzvimbo yaro inotsanangurwa se: S = av, apo, uye-mativi erekete.

Apo zvinosvika pajeri ye quadrangular, nzvimbo yechitsuwa chemajeri akakodzera inorongwa nemutsetse wekona. Nokuti ndiye iye anorara pasi. S = a ² .

Munyaya iyo nheyo yeparallelepiped, kuenzana kunotevera kuchadiwa: S = a * n _a . Izvi zvinoitika kuti rutivi rweparallelepiped runopiwa uye imwe yemakona. Zvino, kuti tiverenge urefu, tinoda kushandisa chimiro chinowedzera: _a = b * sin A. Zvakare, kona A iri pedo ne "c" kurutivi, uye kukwirira kunopesana neizvi.

Kana rhombus iri pamucheto wejeri, uye kuti uone nzvimbo yaro, iyo yakasarudzwa inofanira kudiwa neparallelogram (sezvo iri iyo nyaya chaiyo). Asi isu tinogonawo kushandisa izvi: S = 1 d ₁ d ₂ . Pano d ₁ uye d ₂ ndiwo maviri diagonals e rhombus.

Ruramisa pentagonal prism

Ichi chiitiko chinosanganisira kuparadzanisa polygon mumatatu uye nzvimbo dzacho dziri nyore kudzidza. Kunyangwe izvi zvichiitika kuti zviyero zvinogona kunge zvine nhamba yakasiyana yezvidimbu.

Sezvo nheyo yejeri iri pentagon yenguva dzose, inogona kugoverwa kuva mashanu equilateral triangles. Zvadaro nzvimbo yepasi yejeri iri yakaenzana nenzvimbo imwe yekatatu yakadaro (iyo nzira inogona kuonekwa kumusoro) yakawanda nemashanu.

Ruramisa hexagonal prism

Maererano nenheyo inorondedzerwa kune pentagonal prism, zvinokwanisika kuputsa hexagoni yeganda kusvika ku6 equilateral triangles. Chimiro chemugadziro wekambani yakadaro yakafanana neyo yapfuura. Chero mairi iyo nzvimbo yechinyorwa chekufananidza inofanira kuwedzerwa nematanhatu.

Chirevo chinoratidzika sezvi: S = 3/2 uye ² * √3.

Zvinangwa

№ 1. Yakarurama yakakwana yechirrangular prism inopiwa. Rakakanganiswa iri masendimita 22, kureba kwe polyhedron iri masendimita 14. Funga nzvimbo yechando chejeri uye yose yakareba.

Iyo mhinduro. Nheyo yejeri iri chikamu, asi rutivi rwayo haruna kuzivikanwa. Tsvaga kukosha kwayo kunogona kubva pane diagonal ye square (x), iyo inobatanidza ne diagonal ye prism (d) uye yakakwirira (n). X ² = d ² - n ² . Kune rumwe rutivi, chikamu ichi "x" ndicho chikonzero mumakatatu, makumbo ayo akaenzana nerutivi rwekwere. Ndiko, x ² = a ² + a ² . Saka, zvinosvika kuti ² = (d ² - ² ) / 2.

Kudzorera d ne 22, uye "н" kuti iite panzvimbo yayo ne 14, zvinosvika kuti rutivi rwekona ndeye 12 cm.Zvino zvino ingoona nzvimbo yechando: 12 * 12 = 144 cm ² .

Kuti uzive nzvimbo yepasi rose, unoda kuwedzera kaviri kukosha kwerutivi rwepasi uye nechechina. Iyo yekupedzisira inogona kuwanikwa nyore nyore kubva pakutsvaga kwekatekete: kuwedzera kukwirira kwe polyhedron uye nechemberi kwechitsiko. Ndiko, 14 ne12, nhamba iyi ichaenzana ne168 cm ² . Zvose nzvimbo yejeri iyi 960 cm ² .

Mhinduro. Nzvimbo yepasi pejeri iri 144 cm ² . Iyo yose yakareba 960 cm ² .

Nha. 2. Chirwere chakakosha chetatu chinopiwa. Pasi pedo pakanga pane katatu ine rutivi rwemasendimita matanhatu. Panguva imwe chete, kuwirirana kwebasa rinotarisa rinokwana 10 cm.Cherechedza nzvimbo: nheyo uye inowanikwa pasi.

Iyo mhinduro. Sezvo prism yakarurama, nheyo yaro inonzi equilateral triangle. Nokudaro, nzvimbo yaro yakaenzana nematanhatu mumakiromita akawedzerwa ne ¼ uye nemuganhu wakaenzana we 3. Kuverenga nyore kunotungamirira kumugumisiro: 9√3 cm ² . Iyi ndiyo nzvimbo yechitsuwa chimwe chejeri.

Zvose zvakatarisana zviso zvakatarisa zvakafanana uye zvinomiririra madhikoni ane mativi matanhatu uye 10 cm Kuti uverenge nzvimbo dzazvo, zvakakwana kuti uwedzere nhamba idzi. Zvadaro uvawedzere ivo vatatu, nokuti kune dzakawanda kumativi edges ejeri. Zvadaro nzvimbo ye-lateral pamusoro inokuvadza kusvika pa1 cm ² .

Mhinduro. Nharaunda yacho: nheyo iri 9√3 cm ² , iyo lateral pamusoro pejaya iri 180 cm ² .