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Giải bài 7.35 trang 41 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hình lăng trụ \(ABC \cdot A'B'C'\) có \(A'B'C'\) và \(AA'C'\) là hai tam giác đều cạnh \(a\).

♊Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho hình lăng trụ \(ABC \cdot A'B'C'\) có \(A'B'C'\) và \(AA'C'\) là hai tam giác đều cạnh \(a\). Biết \(\left( {ACC'A'} \right) \bot \left( {A'B'C'} \right)\). Tính theo \(a\) thể tích khối lăng trụ \(ABC \cdot A'B'C'\).

Phương pháp giải - Xem chi tiết

Áp dụng công thức tính thể tích khối lăng trụ: \(S = B.h\). Trong đó: \(B\) là diện tích đa giác đáy \(h\) là đường cao của hình lăng trụ

Lời giải chi tiết

Kẻ \(AH \bot A'C'\) tại \(H\) thì \(AH \bot \left( {A'B'C'} \right)\).Ta có \({S_{A'B'C'}} = \frac{{{a^2}\sqrt 3 }}{4};AH = \frac{{a\sqrt 3 }}{2}\)Suy ra \({V_{ABC.A'B'C'}} = {S_{A'B'C'}} \cdot AH\)\( = \frac{{{a^2}\sqrt 3 }}{4} \cdot \frac{{a\sqrt 3 }}{2} = \frac{{3{a^3}}}{8}\).

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