수학동아 - 폴리매스

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Function: get_footer

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [기하]원에 내접하는 오각형의 넓이 문제

yh36 2020.09.15 03:35 조회 712

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

헤론의 공식은 삼각형의 세 변의 길이를 알 때 그 넓이를 구할 수 있다는 내용이다.

이는 브라마굽타 공식의 특수한 경우로 볼 수 있는데 그것은 한 원에 내접하는 어떤 사각형의 각 변의 길이를 알 때의 넓이 공식이다.

헤론의 공식 : $S = \sqrt{s(s-a)(s-b)(s-c)}$ (단, S는 삼각형의 넓이, a,b,c는 각 변의 길이이고, s = (a+b+c)/2)

브라마굽타의 공식 : $S = \sqrt{(s-a)(s-b)(s-c)(s-d)}$ (단, S는 사각형의 넓이, a,b,c,d는 각 변의 길이이고, s = (a+b+c+d)/2)

한 원에 내접하는 어떤 오각형의 각 변의 길이가 a,b,c,d,e이다.

그렇다면 그 오각형의 넓이는?

이전글 [규칙]SENTTTTTTTTTTTTTTTTTTTT

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