Pehea e huli i ka wahi o ka rhombus?

Pehea e huli i ka wahi o ka rhombus? E haawi aku i ka pane, e pono e ike mua i ka daimana mea mākou noonoo.

Mua, he quadrangle. Ka lua, ka mea i eha likeʻaoʻao. Apana, kona diagonals i ÷ haku i ke kuʻina wahi. Ha, ua māheleʻia ka diagonal kuʻina wahi i like na hapa. Fifthly,ʻo ia kaʻana like 'ana diagonal kihi o ka rhombus i loko o nā māhele like. Ono, ma ka huina o nā pana pua i mea e pili ana i ka kekahiʻaoʻao, e i ka wehe ana ae, huina, a laila 180. A ina e olelo wale, ke daimana - he ihona hene ahalike.

Inā e lawe i ka huinahalike kona aoao i hoʻopaʻaʻia flexibly, a hiki wawe ka huki ia i loko o nā ku pono ana i ka makau, i ke huinahalike, e lilo kona squareness, a huli i loko o ka daimana. No laila, ke daimana me ka pono pana pua - keia mea he maoli huinahalike.

Ka mea mua e hoʻolauna i ka manaʻo ana o daimana Hero a me Pappus o Alexandria, Greek makemakika. Ka hua'ōlelo "daimana" o ka Helene hiki ke unuhi 'ia e like me ka "pahu".

E huli i ka wahi o ka rhombus, ia mea ke kumukuai o ka noonoo ana o ka daimana - mea he parallelogram. hiki ke loaʻa ma ka hoonui waena o ke kumu a me ka wahi o ka parallelogram, i mea o ke kuhikuhi ana a me ke kiekie.

E hoao i kēia, ka mea e hōʻike pū 'ana mai o ka luna o ke keena kihi o ka rhombus p ÷. No ka laʻana, haawiia mai he daimana QWER. Mai na vertices o ka luna kihi Q a me ka W p ÷ QT a me WY. A me ka p ÷ haku QT e kau mai maluna o kaʻaoʻao o RE, a me p ÷ haku WY mea ma luna o ka mau nō o kēiaʻaoʻao.

Penei, hou huli QWYT quadrilateral me ka laua mau aoao a me ka pololei pana pua, a, ma muli o ka keia, ka mea i hiki i ka inoa wiwo ole rectangle.

I ka wahi o keia rectangle ua hoʻonui i kaʻaoʻao a me ke kiekie. Ano, ua pono, e hooiaio ana i ka wahi o ka kūpono rectangle wahi hoʻopili like me ka haawi mai ana o ka daimana.

E noonoo pono i loaa mai ma ka kūkulu hou triangle mauna QYR me ke kuaua, ua hiki ke olelo aku i ka mea, e ana ma ka wāwae, a me ka hypotenuse, Ma hope iho o nā wāwae o nā triangle mauna i lawelawe 'ia ÷ haku, a ma ka mea ia manawa i nāʻaoʻaoʻelua o ka kūpono rectangle. A hypotenuse - kēiaʻaoʻao o ka daimana.

Rhombus o ka huina o ka hale o ka triangle a me ka trapezoid QYR QYEW. Ke kūpono rectangle ua haku o ka ia trapezoid a me ka triangle QYEW ke kuaua, o kona wahi, ua like me ka wahi o ka triangle QYR. Nolaila i ka hopena paipai iho: QWER rhombus wahi waiwai hoʻopili like me ka wahi o ka rectangle QWYT.

Ano ka mea, Ua ike pehea e huli i ka wahi o ka rhombus o kaʻaoʻao a me kona kiekie: e pono e hoonui.

Oe ke loaʻa i ka wahi o ka rhombus, he rhombus e ike ana i ka huina a me ka ao ao o. He mea e pono ai wale, e ike i ka mea o ka sine o ka huina, a me ka hoonui ia ma palua i kaʻaoʻao. E huli i ka sine hiki ke hoʻohana i ka me ka m'kini helu a Bradis papaʻaina.

I kekahi manawa, olelo ai o Iosepa pehea e huli i ka wahi o ka rhombus, hoʻohana 'sine o ka huina a me ke kahahńnai o ka kaiapili kākauʻia i loko o laila, i pono ka i kā mākou.

Eia naʻe, ka hapanui pinepine e huli i ka wahi o ka rhombus ma diagonally. Mai keia haʻilula ka mea, penei i ka wahi mea poluproizvedeniyu diagonals.

Hoao ia ka nani na mea, e noonoo pono i mau triangle mauna QWE a ERQ, i loaa iloko o ka daimana i loko o kekahi diagonal, Mau triangle mauna e like ma ekolu aoao a lalo, a he moku e kihi elua.

Ma hope o Noho i ka lua o ka daimana diagonal, ua loaa i ke kiʻekiʻe o kēia mau triangle mauna, no ka mea, na diagonals intersect i wahi X ma ka huina o ka 90 degere. Ka wahi o ka triangle QWE o ka huina hoonui o QE, i mea hoʻokahi'īniha ma ka WX - hapalua o ka lua diagonally puunaueia e ka mau.

Ano, i ka ninau o ke ana e imi i ka wahi o ka rhombus, i ka pane mea maopopo: kēia 'aoʻao o E e pāpālua. No ka pono o ka lawe ana mai i ka 'aoʻao o algebraic hiki e kekahi diagonal denoted ma ka palapala Z, oiai o ka lua - me ka palapala make. mākou loaʻa:

2 (Z X 1 / 2u: 2) = Z X 1 / 2u, i pono na lau - poluproizvedenie diagonals.