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Câu 11 trang 124 SGK Hình học 11 Nâng cao

Hình tứ diện ABCD có AB, AC, AD đôi một vuông góc là AB = AC = AD = 3. Diện tích tam giác BCD bằng
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Đề bài

Hình tứ diện ABCD có AB, AC, AD đôi một vuông góc là AB = AC = AD = 3. Diện tích tam giác BCD bằng A. \({{9\sqrt 3 } \over 2}\) B. \({{9\sqrt 2 } \over 3}\) C. 27 D. \({{27} \over 2}\)

Lời giải chi tiết

Chọn (A).

Ta có: BC = CD = BD = \(3\sqrt 2 \)Tam giác BCD đều cạnh bằng\(a = 3\sqrt 2 \,nen\,{S_{BCD}} = {{{a^2}\sqrt 3 } \over 4} = {{18\sqrt 3 } \over 4} = {{9\sqrt 3 } \over 2}\)

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