(Thi vào 6 trường Hà Nội Amsterdam 2011 – 2012)
Cho tam giác ABC biết BM = MC; CN = 3 x NA (như hình vẽ) và diện tích tam giác AEN bằng 27 cm². Tính diện tích tam giác ABC?

Lời giải của GV ufaindo.xyz

Nối E với C và B với N

Ta có S_EMC = S_EMB (Chung chiều cao hạ từ đỉnh E và MB = MC)

Lại có S_NMC = S_NMB (Chung chiều cao hạ từ đỉnh N và MB = MC)

Suy ra S_ENC = S_ENB

Ta có S_ENC = 3 x S_AEN🧜 (Chung chiều cao hạn từ đỉnh E và đáy NC = 3 x NA)

Suy ra S_ENC = S_ENB = 3 x 27 = 81 (cm²)

S_BNA = S_ENB - S_AEN = 81 – 27 = 54 (cm²)

Ta có S_ABC = 4 x S_BAN꧅ (Chung chiều cao hạ từ đỉnh B và AC = 4 x AN)

Suy ra S_ABC = 4 x S_BAN= 4 x 54 = 216 (cm²)

Đáp số: 216 cm²

Báo lỗi - Góp ý

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(Thi vào 6 trường Hà Nội Amsterdam 2011 – 2012) Cho tam giác ABC biết BM = MC; CN = 3 x NA (như hình vẽ) và diện tích tam giác AEN bằng 27 cm². Tính diện tích tam giác ABC?

(Thi vào 6 trường Hà Nội Amsterdam 2011 – 2012)
Cho tam giác ABC biết BM = MC; CN = 3 x NA (như hình vẽ) và diện tích tam giác AEN bằng 27 cm². Tính diện tích tam giác ABC?