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Bài 8.26 trang 79 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình lăng trụ tứ giác đều ABCD.A’B’C’D’ có cạnh đáy bằng a
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Đề bài

Cho hình lăng trụ tứ giác đều ABCD.A’B’C’D’ có cạnh đáy bằng a. Gọi M, N, P lần lượt là trung điểm của AD, DC, A’D’. Tính khoảng cách giữa hai mặt phẳng (MNP) và (ACC’).

Phương pháp giải - Xem chi tiết

Khoảng cách giữa 2 mặt phẳng song song là khoảng cách từ 1 điểm bất kì của mặt này đến mặt phẳng kia.

Lời giải chi tiết

Ta có: MN // AC, MP // AA’Nên (MNP) // (ACC’)Nên khoảng cách cần tìm bằng khoảng cách giữa P và (ACC’) và bằng một nửa khoảng cách giữa B và (ACC’)B’O’ vuông góc với A’C’, B’C’ vuông góc với CC’Suy ra B’O’ vuông góc với (ACC’)Nên khoảng cách giữa B và (ACC’) là B’O’ = 1/2B’D’ = \(\frac{{a\sqrt 2 }}{2}\)Vậy khoảng cách cần tìm bằng \(\frac{{a\sqrt 2 }}{4}\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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