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Giải bài 24 trang 14 SBT toán 10 - Cánh diều

Tính số đường chéo của một đa giác lồi có 12 đỉnh.

♏Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

꧃Tính số đường chéo của một đa giác lồi có 12 đỉnh.

Phương pháp giải - Xem chi tiết

Cứ 2 đỉnh bất kì trong đa giác lồi (2 đỉnh không kề nhau) tạo thành một đường chéo của đa giác Bước 1: Tính số đoạn thẳng được tạo từ 2 điểm bất kì của đa giác Bước 2: Tính số cạnh của đa giác lồi

Bước 3: Tính số đường chéo của đa giác lồi bằng hiệu của số đoạn thẳng ở bước 1 và số cạnh của đa giác

Lời giải chi tiết

Đa giác lồi có 12 đỉnh thì có 12 cạnh.Số cách chọn 2 đỉnh trong 12 đỉnh là một tổ hợp chập 2 của 12.Suy ra số cách chọn 2 đỉnh trong 12 đỉnh là: \(C_{12}^2\) cách chọnVậy số đường chéo cần tìm là \(C_{12}^2 - 12 = 54\) 

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