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Çì·ÐÀÇ °ø½Ä(Heron¡Çs Formula), »ï°¢Çü ¸éÀû °è»ê - ¼¼ º¯ÀÇ ±æÀÌ ÀÌ¿ë

ÀÛ¼ºÀÚ Uploader : goodday ÀÛ¼ºÀÏ Upload Date: 2017-10-13º¯°æÀÏ Update Date: 2017-10-13Á¶È¸¼ö View : 3526

Type1 Type2
±×¸²°ú °°ÀÌ »ï°¢Çü ABCÀÇ ¼¼ º¯ÀÇ ±æÀ̸¦ °¢°¢ a, b, c¶ó ÇÏ°í, Á¡ A¿¡¼­ ¼ö¼±À» ³»·Á Á¡ H¸¦ Àâ´Â´Ù.

Á¡ A¿Í Á¡ HÀÇ ±æÀ̸¦ h¶ó ÇÏ°í, Á¡ B¿¡¼­ H±îÁöÀÇ °Å¸®¸¦ x ¶ó ÇÑ´Ù.

ÇÇŸ°í¶ó½ºÀÇ Á¤¸®¿¡ µû¶ó, ´ÙÀ½°ú °°ÀÌ h ¸¦ ±¸ÇÒ ¼ö ÀÖ´Ù.

h©÷ = c©÷ - x©÷ = b©÷ - (a - x)©÷

c©÷ - x©÷ = b©÷ - a©÷ + 2ax - x©÷

c©÷ = b©÷ - a©÷ + 2ax

x = ( c©÷ - b©÷ + a©÷ ) / (2a)

h©÷ = c©÷ - x©÷ = c©÷ - ( c©÷ - b©÷ + a©÷ )©÷ / (4a©÷)

    = (4a©÷c©÷ - ( c©÷ - b©÷ + a©÷ )©÷) / (4a©÷)

    = (2ac + c©÷ - b©÷ + a©÷ )(2ac - c©÷ + b©÷ - a©÷) / (4a©÷)

    = ((a+c)©÷ - b©÷ )(b©÷ - (a-c)©÷) / (4a©÷)

h = (1/(2a))*((a+c-b)(a+c+b)(b+a-c)(b-a+c))^(1/2)

  = (1/(2a))*((a+b+c)(b+c-a)(a+c-b)(a+b-c))^(1/2)

»ï°¢ÇüÀÇ ¸éÀû S = (1/2)ah À̹ǷÎ,

S = (1/4)*((a+b+c)(b+c-a)(a+c-b)(a+b-c))^(1/2)

S = ((a+b+c)(b+c-a)(a+c-b)(a+b-c) / 16)^(1/2)

s = (a+b+c)/2 ¶ó Çϸé,

S = (s(s-a)(s-b)(s-c))^(1/2)
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