Sida loo xisaabiyo degaanka ee Ahraamta ah: saldhig, dhinaca oo waxaa ka buuxda?

In diyaarinta imtixaanka ee ardayda xisaabta u leeyihiin in ay nidaaminta aqoonta algebra iyo joomatari. Waxaan jeclaan lahaa in la isu geeyo dhammaan macluumaadka loo yaqaan, sida sida loo xisaabiyo degaanka ee Ahraamta ah. Waxaa intaa dheer, laga bilaabo hoose iyo dhinaca wajahaya ilaa degaanka dusha oo dhan. Haddii kooxda ku timaaddo xaalad ah waa mid cad, sida ay yihiin saddexagal, ee saldhiga ah waa had iyo jeer kala duwan.

Sida loo noqon marka degaanka ee salka Ahraamta?

Waxay noqon kartaa tirada arrin kasta oo ka xagalka ah aan sabab lahayn in ay n-gon ah. Oo tanu waxay saldhig, farqiga tirada xaglo marka laga reebo, waxaa laga yaabaa in tirada saxda ah ama aan sax ahayn. In danta ardayda hawlaha on imtixaanka laga helay shaqooyin oo keliya tirada saxda ah ee salka. Sidaa darteed, waxaan ka hadli doonaa oo kaliya iyaga oo ku saabsan.

xagalka isle

Taasi waa isle. Mid ka mid ah in dhammaan dhinacyada siman yihiin oo loo soo xarafka "a". Xaaladdan oo kale, meesha salka of Ahraamta ah waxaa loo xisaabiyaa by formula ah:

S = (a ² * √3) / 4.

square

formula The si ay u xisaabiso ay meesha waa fudud, waa "a" - side mar kale waa:

Oo S = ^2.

n-gon caadiga ah Sabab La'aan

Marka dhinac ee geesoolayaasha magaca la mid ah. Waayo, tirada xaglaha loo isticmaalo warqad n Latin.

S = (n * ^{2 a)} / (4 tg * (180º / n)) .

Sidee inay soo galaan xisaabinta of degaanka ee dusha sare lateral oo buuxa?

Tan iyo markii tirada salka sax yahay, markaas oo dhan Wajiyada Ahraamta waa u siman yihiin. Mid kasta oo ka kaas oo ah saddex-xagalka ah oo labaale ah, tan iyo geesaha dhinaca siman yihiin. Markaas, si ay u xisaabiso degaanka ee kooxda ka mid ah Ahraamta baahan formula ka kooban wadarta monomials isku mid. Tirada la eego waxaa lagu go'aamiyaa tirada dhinac salka.

bedka saddex xagal ah oo labaale ah waxa lagu xisaabiyaa by formula, taas oo kala badh ka mid ah wax soo saarka ee saldhiga ah lagu dhufto sarajooggiisuna. Tani height ee Ahraamta yeedhay apothem. Its naqshada - "A". formula guud ee aagga of dusha lateral waa sida soo socota:

S = ½ P * A, halkaas oo P - wareegga kore ee salka Ahraamta.

Waxaa jira jeer marka aan la og yahay in kooxdiisa ay salka, laakiin geesaha dhanka yihiin (a) guri iyo xagal ee Cardiff (α). Markaasaa waxaa u ku tiirsan isticmaasho formula ee soo socda si ay u xisaabiso aagga lateral of Ahraamta:

S = n / 2 ilaa ² * α dembi.

Task № 1

Xaaladda. Raadi aagga guud ee Ahraamta, haddii salkeeda waa xagalka ah isle kooxda a of 4 cm oo uu qiimo √3 apothem cm ah.

Go'aan. Waa in lagu bilaabo xisaabinta wareega salka. Tan iyo markii ay tani tahay xagal boos joogta ah, ka dibna P = 3 * 4 = 12 cm apothem Sida la og yahay, mid ka mid ah isla markiiba xisaabi kartaa aagga of dushiisa oo dhan lateral :. ½ * 12 * √3 = 6√3 ^cm2.

Si aad u hesho xagal ee saldhiga ah waa qiimaha degaanka (4 ² * √3) / 4 = 4√3 ^cm2.

Si loo go'aamiyo goobta oo dhan u baahan yihiin inay isku laab labada qiimaha keentay: 6√3 + 4√3 = 10√3 ^cm2.

Jawaab. 10√3 ^cm2.

Dhibaatada № 2

Xaaladda. Waxaa jira Ahraamta ah quadrangular joogto ah. oo saldhig kasta dhererkiisu waa loo siman yahay ilaa 7 mm, ku laayeen lateral - 16 mm. Waxaad u baahan tahay in la ogaado bedka ay.

Go'aan. Tan iyo polyhedron ah - qaab ah oo sax ah, at salkeeda waa square ah. Maqalka aagga saldhiga oo dhinac lateral awoodaan inay tiriyaan Ahraamta oo laba jibbaaran. formula ee square waxaa sare lagaa siin. Oo anna waxaan ogahay oo dhan Wajiyada dhinac ee saddexagalka. Sidaa darteed, waxaad isticmaali kartaa caanaha iyo haadbiyoodda ee xisaabinta meelaha ay.

The ugu horeysay ee xisaabinta waa mid fudud oo u wadin inuu soo lambarkan: 49 mm ^2. Si loo xisaabiyo qiimaha labaad u baahan tahay semiperimeter: (7 + 16 * 2): 2 = 19.5 mm. Haddaba inaan xisaabino bedka saddex xagal ah oo labaale ah: √ (19,5 * (19,5-7) * (19,5-16) ²⁾ = √2985,9375 = 54.644 mm ^2. Waxaa jira afar saddexagal, si marka la xisaabinayo tirada ugu dambeeya ee u baahan doontaa inaad sii bataan by 4.

Helay: 49 + 4 * 54,644 = 267,576 ^mm2.

Jawaab. 267,576 qiimaha la doonayo of ² mm.

Task № 3

Xaaladda. At Ahraamta quadrangular si joogto ah loo baahan yahay si ay u xisaabiso aagga. Waxaa la og yahay dhinac oo square ah - 6 cm iyo height - 4 cm.

Go'aan. Habka ugu fudud ee ay u isticmaalaan caanaha si ay wax soo saarka oo ka mid ah wareega iyo apothem. Qiimaha ugu horeysay waxaa laga helaa si fudud. The labaad wax yar adag.

Waxaan leenahay doontaa in la xasuusto Aragtida ku Theorem oo ka fiirso xagal midig. Waxaa la aasaasay by height of the Ahraamta iyo apothem, taas oo shakaal. Lugta labaad waa kooxda kala bar ka mid ah laba jibbaaran, sida height polyhedron dhaco dhexe waxaa ka mid ah.

apothem Manaystay (shakaal xagal midig) waa loo siman yahay si √ (March ² + 4 ²⁾ = 5 (cm).

Haddaba waxaa suurtagal ah in loo xisaabiyo qiimaha la doonayo: ½ * (4 * 6) * 5 + 6 ² = 96 (cm ^2).

Jawaab. 96 cm ^2.

Dhibaatada № 4

Xaaladda. Dana Ahraamta hexagonal joogto ah. The dhinac ee salkeeda loo siman yahay 22 mm, cidhifyada lateral - 61 mm. Waa maxay aagga of dusha lateral of polyhedron this?

Go'aan. sababaynta ku dhex jira waa isku mid sida ku cad №2 hawsha. Kaliya Ahraamta halkaasuu ku siiyey in ay laba jibbaaran salka, iyo haatan waa geesle.

Tallaabada ugu horreysa waxaa la xisaabaa ayadoo aagga saldhiga oo ah caanaha ee kor ku xusan ^{(6 * 22 2) / (ka} 4 tg * (180º / 6)) = 726 / (tg30º) = 726√3 ^cm2.

Haddaba waxaad u baahan tahay si aad u hesho nus-wareega ah ee saddex xagalka ah oo labaale ah, taas oo ah dhinaca wajiga. (22 + 61 * 2) :. = 72 cm 2 weli on formula haadbiyoodda ee loo xisaabiyo bedka mid kasta oo saddexagalka, ka dibna waxa ay u badin by lix laab iyo mid ka mid ah in ka leexatay in ay salka.

Xisaabaha on formula haadbiyoodda ee: √ (72 * (72-22) * ( 72-61) 2) = √435600 = 660 cm ^2. Xisaabaha ayaa bixin doona bedka lateral: 660 * 6 = 3960 cm ^2. Waxaa weli si ay u dar ilaa si aad u ogaato dushiisa oo dhan: 5217,47≈5217 cm ^2.

Jawaab. Sababaha - 726√3 cm ^2, dusha dhinaca - 3960 cm ^2, meesha oo dhan - 5217 cm ^2.