Me pēhea te whakamahi i te Tātai a Heron
Ko te tātai a Heron he tikanga pāngarau e whakamahia ana hei tatau i te horahanga o tētahi tapatoru ina mōhiotia te roa o ngā taha e toru. I tapaina te tikanga i muri i te tohunga pāngarau Kariki, a Hero o Alexandria. I roto i tēnei tuhinga, ka hipokina e mātou te tātai a Heron i roto i ngā taipitopito, taahiraa i te taahiraa, kia mārama ai koe, kia ngāwari ai hoki te whakatinana i roto i ō tataunga.
He Kupu Whakataki ki te Tātai a te Mātuku
I te nuinga o te wā, mā te tātai a Heron ka taea e tātou te kimi i te horahanga o te tapatoru mā te mōhio noa ki te roa o ōna taha e toru, me te kore e tatau i te teitei i te tuatahi. Ka taea te whakaatu i te tātai a Heron mō te horahanga o te tapatoru penei:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
Ko \( a \), \( b \), me \( c \) ngā roa o ngā taha o te tapatoru, ā, ko \( s \) te haurua-pānga o te tapatoru i tatauhia mā te whakamahi i te tātai:
\[ s = \frac{a + b + c}{2} \]
Ngā Hipanga hei Whakamahi i te Tātai a Heron
1. Te Tāutu i te Roa o ngā Taha e Toru o te Tapatoru
Ko te taahiraa tuatahi ki te whakamahi i te tātai a Heron ko te mōhio ki te roa o ngā taha e toru o te tapatoru e hiahia ana koe ki te tatau i te horahanga. Me kī he tapatoru tā tātou me ngā taha he roa \( a \), \( b \), me \( c \).
Tauira: Me kī he roa ngā taha o tētahi tapatoru ko \( a = 7 \) cm, \( b = 8 \) cm, me \( c = 5 \) cm.
2. Te Tātai i te Hauwhā-ā-rohe (\( s \))
I muri i te mōhio ki te roa o ngā taha e toru, me tatau tātou i te haurua-pōtae (\(s \)) o te tapatoru. Ko te haurua-pōtae he haurua o te pōtae o te tapatoru. Ko te tātai mō te tatau i te haurua-pōtae ko:
\[ s = \frac{a + b + c}{2} \]
Tauira: Mā te roa o ngā taha \( a = 7 \) cm, \( b = 8 \) cm, me \( c = 5 \) cm, ka tatauhia te haurua-pānga penei:
\[ s = \frac{7 + 8 + 5}{2} = \frac{20}{2} = 10 \text{ cm} \]
3. Te Whakahiato i te Tātai a Heron
I muri i te tatau i te haurua-pānga, ka taea e tātou te hanga i te tātai a Heron hei tatau i te horahanga o te tapatoru. Ko te tātai a Heron e kīia ana penei:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
4. Te tatau (sa), (sb), (sc)
Tirohia ia wāhanga i roto i te tātai a Heron. Tuatahi, tatauhia ngā uara o \( (sa), (sb), \) me \( (sc) \):
Tauira:
\[ s – a = 10 – 7 = 3 \]
\[ s – b = 10 – 8 = 2 \]
\[ s – c = 10 – 5 = 5 \]
5. Whakakapia ngā Uara ki roto i te Tātai
Kia kitea ngā uara o \( (sa), (sb), \) me \( (sc) \), whakakapia ēnei uara ki te tātai a Heron hei tatau i te horahanga o te tapatoru:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
\[ \text{Horahanga} = \sqrt{10 \times 3 \times 2 \times 5} \]
6. Te Whakangāwari i ngā Kīanga
Whakangāwaritia te kīanga:
\[ \text{Horahanga} = \sqrt{10 \times 3 \times 2 \times 5} \]
\[ \text{Horahanga} = \sqrt{300} \]
\[ \text{Horahanga} \approx 17.32 \text{ cm}^2 \]
Nō reira, ko te horahanga o tētahi tapatoru me ōna taha he 7 henimita, he 8 henimita, me te 5 henimita, tata ki te 17.32 henimita².
He aha i whakamahia ai te Tātai a Heron?
He maha ngā painga o te tātai a Heron, ā, he mea tino whai hua tēnei i roto i te āhuahanga, inā koa mō te tatau i te horahanga o te tapatoru ina kore e mōhiotia te teitei o te tapatoru.
1. Ngāwari o te Whakamahi
Ko tētahi o ngā painga matua o te tātai a Heron ko tōna māmā noa iho. Kāore koe e hiahia ki te ine i te teitei o te tapatoru. Mā te mōhio noa ki te roa o ngā taha e toru, ka taea e koe te tatau tonu i tōna horahanga.
2. Ngāwari
He tino ngāwari te tātai a Heron nā te mea ka taea te whakamahi ki tētahi momo tapatoru, tae atu ki ngā tapatoru unahi (e toru ngā taha he rerekē te roa), ngā tapatoru rite-waewae (e rua ngā taha he ōrite te roa), me ngā tapatoru ōrite-taha (e toru ngā taha he ōrite te roa).
3. Whānui te Whakamahinga
He whānuitia ngā whakamahinga o te tātai a Heron i roto i ngā momo mara, tae atu ki te hangarau, te hoahoanga, te whetū, tae atu ki te toi. He tino whai hua tēnei tātai ina hiahia koe ki te kimi i te horahanga o te tapatoru.
He Tauira anō e Whakamahi ana i te Tātai a Heron
Hei whakahōhonu ake i tō tātou māramatanga, me titiro tātou ki tētahi atu tauira. Me kī he tapatoru tā tātou me ngā taha \( a = 9 \) cm, \( b = 12 \) cm, me \( c = 15 \) cm.
Hipanga 1: Te Tātai i te Āwhiowhio (\(s \))
\[ s = \frac{a + b + c}{2} \]
\[ s = \frac{9 + 12 + 15}{2} = \frac{36}{2} = 18 \text{ cm} \]
Hipanga 2: Tātaihia (sa), (sb), me (sc)
\[ s – a = 18 – 9 = 9 \]
\[ s – b = 18 – 12 = 6 \]
\[ s – c = 18 – 15 = 3 \]
Hipanga 3: Whakakapia ngā Uara ki roto i te Tātai
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
\[ \text{Horahanga} = \sqrt{18 \times 9 \times 6 \times 3} \]
Hipanga 4: Te Whakangāwari i te Kīanga
\[ \text{Horahanga} = \sqrt{18 \times 9 \times 6 \times 3} \]
\[ \text{Horahanga} = \sqrt{2916} \]
\[ \text{Horahanga} \approx 54 \text{ cm}^2 \]
Nō reira, ko te horahanga o tētahi tapatoru me ōna taha he 9 henimita, he 12 henimita, me te 15 henimita, tata ki te 54 henimita².
Whakamutunga
He taputapu pāngarau kaha te tātai a Heron mō te tatau i te horahanga o tētahi tapatoru mā te whakamahi noa i te roa o ōna taha e toru. Mā ngā mahi kua whakarārangihia i roto i tēnei tuhinga ka whakaratohia he aratohu mārama, ngāwari hoki mō te whakamahi i tēnei tātai i roto i ngā āhuatanga maha. Mā te mahi poto, ka ngāwari te mōhio ki tēnei tikanga, ā, ka whakamahia hoki ki ō raruraru āhuahanga.
Ehara i te mea he taputapu pāngarau noa iho, engari e whakaatu ana te tātai a Heron i te ataahua me te māmā o te āhuahanga, e whakakotahi ana i ngā huānga taketake i roto i te huarahi whai hua me te whai hua. Ko te tumanako ka āwhina tēnei aratohu i a koe ki te mārama me te whakamahi i te tātai a Heron me te maia me te tika.
