Te Tātai i te Horahanga o te Tapatoru: Ngā Tikanga, Ngā Tauira, me Ngā Whakamahinga i te Oranga o Ia Rā
Ko te tatau i te horahanga o te tapatoru he ariā taketake i roto i te pāngarau e whakaurua ana ki te kura tuatahi. Ko ngā tapatoru, hei tētahi o ngā āhua ā-ira taketake, he whānuitia te whakamahinga i roto i te ao mātauranga me te ao o ia rā. Ka arotakehia e tēnei tuhinga ētahi tikanga mō te tatau i te horahanga o te tapatoru, ka hoatu he tauira, ā, ka whakamāramahia ngā whakamahinga mahi o ēnei tataunga.
1. Pendahuluan
He tapatoru he porowhita e toru ōna taha, e toru hoki ōna koki. He maha ngā momo tapatoru e hangai ana ki te roa o ōna taha me ōna koki, pērā i te tapatoru ōrite, te tapatoru rite, te tapatoru rite, te tapatoru matau, me te tapatoru koi. Ehara i te mea he mea nui te tatau i te horahanga o te tapatoru i roto i te pāngarau anake, engari he mea whai hua anō hoki i roto i ngā momo mara pērā i te hoahoanga, te hangarau, me te toi.
2. Tikanga mō te Tatau i te Horahanga o te Tapatoru
2.1 Te Whakamahi i ngā Tātai Taketake
Ko te tātai taketake mō te tatau i te horahanga o te tapatoru ko:
\[ \text{Horahanga} = \frac{1}{2} \times \text{base} \times \text{teitei} \]
Dimana:
– ko te turanga te roa o te taha raro o te tapatoru.
– ko te teitei te tawhiti poutū mai i te turanga ki te tihi o te tapatoru.
Tauira tauira:
Mehemea he tapatoru tā tātou, e 8 cm te roa o te turanga, e 5 cm te teitei. Kātahi ka taea te tatau i tōna horahanga penei:
\[ \text{Horahanga} = \frac{1}{2} \times 8 \, \text{cm} \times 5 \, \text{cm} = 20 \, \text{cm}^2 \]
2.2 Te Whakamahi i te Tātai a Heron
Ka whakamahia te tātai a Heron hei tatau i te horahanga o tētahi tapatoru ina mōhiotia te roa o ngā taha e toru. Ko te tātai ko:
\[ s = \frac{a + b + c}{2} \]
\[ \kuputuhi{Horahanga} = \sqrt{s \times (s – a) \times (s – b) \times (s – c)} \]
Dimana:
– ko a, b, c ngā roa o ngā taha o te tapatoru.
– ko s te haurua o te paenga o te tapatoru.
Tauira tauira:
Mehemea he tapatoru tā tātou, ko ngā taha he 7 henimita, he 8 henimita, me te 9 henimita. Kātahi ka taea te tatau i tōna horahanga penei:
\[ s = \frac{7 + 8 + 9}{2} = 12 \]
\[ \kuputuhi{Horahanga} = \sqrt{12 \times (12 – 7) \times (12 – 8) \times (12 – 9)} = \sqrt{12 \times 5 \times 4 \times 3} = \sqrt{720} \approx 26.83 \, \kuputuhi{cm}^2 \]
2.3 Te Whakamahi i te Pānga-toru
Mena he tapatoru tātau me ngā taha e rua, ā, he koki kei waenganui i aua taha e rua, ka taea te tatau i tōna horahanga mā te whakamahi i te tātai tapatoru:
\[ \text{Horahanga} = \frac{1}{2} \times a \times b \times \sin(C) \]
Dimana:
– ko a, b ngā roa o ngā taha e rua o te tapatoru.
– Ko C te rahi o te koki e karapotia ana e ngā taha a me b.
Tauira tauira:
Mehemea he tapatoru tā tātou, e 6 henimita te whānui me te 8 henimita te whānui o ngā taha, ā, e 45 nekehanga te koki i waenganui i a rāua. Kātahi ka taea te tatau i tōna horahanga penei:
\[ \text{Horahanga} = \frac{1}{2} \times 6 \, \text{cm} \times 8 \, \text{cm} \times \sin(45^\circ) = 24 \times \frac{1}{\sqrt{2}} = 24 \times 0.707 \approx 16.97 \, \text{cm}^2 \]
3. Ngā Whakamahinga i roto i te Oranga o Ia Rā
3.1 Te Hanganga me te Hanganga
He pūkenga nui te tatau i te horahanga o te tapatoru i roto i te hoahoanga me te hanga. Ahakoa he tuanui tapatoru te hoahoa, he piriti cantilever, he hanganga rānei, mā te mōhio ki te tatau tika i te horahanga ka āwhina i te pumau me te whai hua o ngā rauemi.
3.2 Hangarau
I roto i te hangarau, ka taea te whakamahi i te horahanga o te tapatoru i roto i te tātari hanganga, te miihini, me te hoahoa o ngā wāhanga rerekē. Hei tauira, i roto i te tātari i te kaha o ngā rauemi i ngā pūwāhi motuhake, ka whakaarohia he tapatoru hei whakahaere i ngā tataunga.
3.3 Te Whenua me te Mahere Whenua
I roto i te hanga mapi me te ruri whenua, ka whakamahia ngā tapatoru hei tatau i ngā horahanga koretake. Ko te tikanga o te tapatoru, e whakamahi ana i ngā tapatoru hei tatau i ngā tawhiti kāore e taea te ine tika, he whakamahinga anō hoki o te horahanga o ngā tapatoru.
3.4 Toi me te Hoahoa
I roto i te toi me te hoahoa, he maha ngā motika me ngā hanganga āhuahanga e whakamahi ana i te ariā o ngā tapatoru. Mā te mārama ki te horahanga o te tapatoru ka āwhina i ngā kaihoahoa ki te waihanga mahi toi me ngā ōwehenga tika me ngā tatau rauemi whai hua.
4. Ngā Wero me ngā Hapa Noa
4.1 Hapa Ine
Ko tētahi o ngā wero nui ki te tatau i te horahanga o tētahi tapatoru ko te tika o te ine. Mēnā he iti noa ngā hapa i te ine i te turanga, i te teitei rānei, ka nui pea ngā hapa i te horahanga whakamutunga.
4.2 Hapa Tātaitanga
Mā te kore mārama ki tētahi tātai, ki tētahi taahiraa tatau rānei ka puta he hapa. Hei tauira, mā te tatau hē i te (ngā) haurua-porowhita i roto i te tātai a Heron ka puta he horahanga hē.
4.3 Te Whakamahinga Hē o te Ine Taurite
I te whakamahi i ngā tātai pātoru, he mea nui kia whakarite ko te koki e whakamahia ana ko te koki i waenganui i ngā taha e rua e mōhiotia ana. Mā te whakauru i te koki hē, te whakamahi rānei i tētahi koki hē ka puta he hua hē.
5. Whakamutunga
He ariā taketake te tatau i te horahanga o te tapatoru i roto i te pāngarau, ā, he maha ngā whakamahinga o ia rā. Mā te mārama ki ngā tikanga rerekē e wātea ana—ahakoa mā te whakamahi i te tātai taketake, te tātai a Heron, te tātai-ira rānei—ka taea te tatau i te horahanga o te tapatoru i raro i ngā āhuatanga rerekē.
Ehara i te mea ka whakapai ake i ngā pūkenga pāngarau anake te mārama ki tēnei ariā, engari he mea nui anō hoki ki ngā momo mara ngaio, tae atu ki te hoahoanga, te miihini, te whenua, me te toi. Ko te karo i ngā hapa noa me te pupuri i ngā ine me ngā tātaitanga tika te mea nui ki te whakatutuki i ngā hua tika. Ko te tumanako, ka āwhina tēnei arotake i ngā kaipānui ki te mārama ake me te whakamahi i te ariā o te tātai i te horahanga o te tapatoru.
