Pehea e hoʻohana ai i ke ʻano o Heron
ʻO ke ʻano hana a Heron kahi ʻano hana makemakika i hoʻohana ʻia e helu i ka ʻāpana o kahi huinakolu ke ʻike ʻia ka lōʻihi o nā ʻaoʻao ʻekolu. Ua kapa ʻia ke ʻano hana ma hope o ka makemakika Helene ʻo Hero o Alexandria. Ma kēia ʻatikala, e uhi mākou i ke ʻano hana a Heron me nā kikoʻī, kēlā me kēia ʻanuʻu, i hiki iā ʻoe ke hoʻomaopopo a hoʻokō maʻalahi iā ia i kāu mau helu.
Hoʻolauna i ke ʻano hana a Heron
Ma keʻano laulā, hiki i ke ʻano hana a Heron ke ʻike i ka wahi o kahi huinakolu ma ka ʻike wale ʻana i ka lōʻihi o kona mau ʻaoʻao ʻekolu, me ka ʻole o ka helu mua ʻana i ke kiʻekiʻe. Hiki ke ʻōlelo ʻia ke ʻano hana a Heron no ka wahi o kahi huinakolu penei:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
ʻO \( a \), \( b \), a me \( c \) nā lōʻihi o nā ʻaoʻao o ka huinakolu, a ʻo \( s \) ka hapalua-perimeter o ka huinakolu i helu ʻia me ka hoʻohana ʻana i ke ʻano:
\[ s = \frac{a + b + c}{2} \]
Nā ʻanuʻu e hoʻohana ai i ke ʻano o Heron
1. Ke ʻike ʻana i ka lōʻihi o nā ʻaoʻao ʻekolu o kahi huinakolu
ʻO ka hana mua i ka hoʻohana ʻana i ke ʻano hana a Heron, ʻo ia ka ʻike ʻana i ka lōʻihi o nā ʻaoʻao ʻekolu o ka huinakolu nona ka ʻāpana āu e makemake ai e helu. Manaʻo mākou he huinakolu kā mākou me nā ʻaoʻao o ka lōʻihi \( a \), \( b \), a me \( c \).
Laʻana: Manaʻo ʻia he ʻaoʻao ko ka huinahā he \( a = 7 \) kenimika, \( b = 8 \) kenimika, a me \( c = 5 \) kenimika.
2. Ke helu ʻana i ka Semiperimeter (\( s \))
Ma hope o ka ʻike ʻana i ka lōʻihi o nā ʻaoʻao ʻekolu, pono mākou e helu i ka semiperimeter (\(s \)) o ka huinakolu. ʻO ka semiperimeter ka hapalua o ka perimeter o ka huinakolu. ʻO ke ʻano hana no ka helu ʻana i ka semiperimeter penei:
\[ s = \frac{a + b + c}{2} \]
Laʻana: Me nā lōʻihi ʻaoʻao \( a = 7 \) kenimika, \( b = 8 \) kenimika, a me \( c = 5 \) kenimika, helu mākou i ka semiperimeter penei:
\[ s = \frac{7 + 8 + 5}{2} = \frac{20}{2} = 10 \text{ kenimika} \]
3. Ke hōʻuluʻulu ʻana i ka Formula a Heron
Ma hope o ka helu ʻana i ka semiperimeter, hiki iā mākou ke kūkulu i ke ʻano hana a Heron e helu ai i ka ʻāpana o kahi huinakolu. Ua ʻōlelo ʻia ke ʻano hana a Heron penei:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
4. Ke helu ʻana (sa), (sb), (sc)
E nānā i kēlā me kēia ʻāpana i loko o ke ʻano hana a Heron. ʻO ka mea mua, e helu i nā waiwai o \( (sa), (sb), \) a me \( (sc) \):
laʻana:
\[ s – a = 10 – 7 = 3 \]
\[ s – b = 10 – 8 = 2 \]
\[ s – c = 10 – 5 = 5 \]
5. Hoʻololi i nā waiwai i loko o ke Formula
Ke loaʻa iā mākou nā waiwai o \((sa), (sb), \) a me \((sc) \), e hoʻololi i kēia mau waiwai i loko o ke ʻano hana a Heron e helu ai i ka ʻāpana o ka huinakolu:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
\[ \text{ʻĀpana} = \sqrt{10 \times 3 \times 2 \times 5} \]
6. Hoʻomaʻalahi i nā Hōʻike
E hoʻomaʻalahi i ka ʻōlelo:
\[ \text{ʻĀpana} = \sqrt{10 \times 3 \times 2 \times 5} \]
\[ \text{ʻĀpana} = \sqrt{300} \]
\[ \text{ʻĀpana} \approx 17.32 \text{ kenimika}^2 \]
No laila, ʻo ka nui o kahi huinakolu me nā ʻaoʻao o 7 kenimika, 8 kenimika, a me 5 kenimika ma kahi o 17.32 kenimika².
No ke aha e hoʻohana ai i ke ʻano o Heron?
He nui nā pono o ke ʻano hana a Heron e lilo ai ia i mea pono loa i ka geometry, ʻoiai no ka helu ʻana i ka ʻāpana o kahi huinakolu ke ʻike ʻole ʻia ke kiʻekiʻe o ka huinakolu.
1. Ka maʻalahi o ka hoʻohana ʻana
ʻO kekahi o nā pono nui o ke ʻano hana a Heron ʻo ia kona maʻalahi. ʻAʻole pono ʻoe e ana i ke kiʻekiʻe o kahi huinakolu. Ma ka ʻike wale ʻana i ka lōʻihi o nā ʻaoʻao ʻekolu, hiki iā ʻoe ke helu koke i kona ʻāpana.
2. Ka maʻalahi
He maʻalahi loa ke ʻano hana a Heron no ka mea hiki ke hoʻohana ʻia ma kekahi ʻano o ka huinakolu, me nā huinakolu scalene (ʻekolu ʻaoʻao o nā lōʻihi like ʻole), nā huinakolu isosceles (ʻelua ʻaoʻao o ka lōʻihi like), a me nā huinakolu equilateral (ʻekolu ʻaoʻao o ka lōʻihi like).
3. Hoʻohana ākea
He nui nā hoʻohana o ke ʻano hana a Heron ma nā ʻano like ʻole, me ke ʻenekinia, ke kuhikuhipuʻuone, ka ʻike hōkū, a me ke akamai hoʻi. I kēlā me kēia manawa e pono ai ʻoe e ʻimi i ka ʻāpana o kahi huinakolu, he mea pono loa kēia ʻano hana.
ʻO kekahi laʻana e hoʻohana ana i ka Formula a Heron
I mea e hoʻoikaika ai i ko kākou ʻike, e nānā kākou i kekahi laʻana ʻē aʻe. Manaʻo mākou he huinakolu ko kākou me nā ʻaoʻao \( a = 9 \) cm, \( b = 12 \) cm, a me \( c = 15 \) cm.
KaʻAnuʻu Hana 1: Ke Helu ʻana i ka Semiperimeter (\(s \))
\[ s = \frac{a + b + c}{2} \]
\[ s = \frac{9 + 12 + 15}{2} = \frac{36}{2} = 18 \text{ kenimika} \]
KaʻAnuʻu Hana 2: E helu i ka (sa), (sb), a me ka (sc)
\[ s – a = 18 – 9 = 9 \]
\[ s – b = 18 – 12 = 6 \]
\[ s – c = 18 – 15 = 3 \]
KaʻAnuʻu Hana 3: Hoʻololi i nā Waiwai i loko o ke Formula
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
\[ \text{ʻĀpana} = \sqrt{18 \times 9 \times 6 \times 3} \]
KaʻAnuʻu Hana 4: Hoʻomaʻalahi i ka Hōʻike
\[ \text{ʻĀpana} = \sqrt{18 \times 9 \times 6 \times 3} \]
\[ \text{ʻĀpana} = \sqrt{2916} \]
\[ \text{ʻĀpana} \approx 54 \text{ kenimika}^2 \]
No laila, ʻo ka nui o kahi huinakolu me nā ʻaoʻao o 9 kenimika, 12 kenimika, a me 15 kenimika ma kahi o 54 kenimika².
Ka hopena
He mea hana makemakika ikaika ka haʻilula a Heron no ka helu ʻana i ka ʻāpana o kahi huinakolu me ka hoʻohana wale ʻana i ka lōʻihi o kona mau ʻaoʻao ʻekolu. Hāʻawi nā ʻanuʻu i hōʻike ʻia ma kēia ʻatikala i kahi alakaʻi maopopo a maʻalahi hoʻi no ka hoʻopili ʻana i kēia haʻilula i nā kūlana like ʻole. Me kahi hoʻomaʻamaʻa liʻiliʻi, e maʻalahi ʻoe e aʻo i kēia ʻano hana a hoʻopili iā ia i kāu mau pilikia geometry.
ʻOi aku ma mua o kahi mea hana makemakika, hōʻike ke ʻano hana a Heron i ka nani a me ka maʻalahi o ke geometry, e hoʻohui pū ana i nā mea kumu i kahi ala pono a kūpono hoʻi. Manaʻolana mākou e kōkua kēia alakaʻi iā ʻoe e hoʻomaopopo a hoʻopili i ke ʻano hana a Heron me ka hilinaʻi a me ka pololei.
