Cho tam giác ABC có diện tích 90cm2. M là điểm chính giữa cạnh AB. Trên cạnh AC lấy điểm N sao cho AN = 2NC. Tính diện tích tam giác AMN.
K
Khách
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Những câu hỏi liên quan
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29 tháng 8 2015
Diện tích tam giác AMN là:
160:2:4=20 (cm2)
Đáp số:20 cm2
23 tháng 3 2018
nối C với M.
tam giác ACM và tam giác ACB cho chung đường cao hạ tự điểm C xuống cạnh AB. đáy \(AM=\frac{1}{2}\)đáy AB (là điểm chính giữa của cạnh AB)
\(\Rightarrow S_{\left(ACM\right)}=\frac{1}{2}.S_{\left(ABC\right)}=\frac{1}{2}.60=80\left(cm^2\right)\)
xét tam giác AMN và tam giác ACM có chung chiều cao hạ từ M xuống cạnh AC; đáy \(AN=\frac{1}{4}\)đáy AC
\(\Rightarrow S_{\left(AMN\right)}=\frac{1}{4}.S_{\left(ACM\right)}=\frac{1}{4}.80=20\left(cm^2\right)\)
Lời giải:
Ta có:
\(\frac{S_{AMN}}{S_{ABN}}=\frac{AM}{AB}=\frac{1}{2}\) (do $M$ là trung điểm $AB$)
\(\frac{S_{ABN}}{S_{ABC}}=\frac{AN}{AC}=\frac{AN}{AN+NC}=\frac{2NC}{2C+NC}=\frac{2NC}{3NC}=\frac{2}{3}\)
Suy ra:
\(\frac{S_{AMN}}{S_{ABN}}\times \frac{S_{ABN}}{S_{ABC}}=\frac{1}{2}\times \frac{2}{3}\)
\(\frac{S_{AMN}}{S_{ABC}}=\frac{1}{3}\)
\(S_{AMN}=\frac{1}{3}\times S_{ABC}=\frac{1}{3}\times 90=30\) (cm2)
Hình vẽ:
![](data:image/png;base64,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)