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AN = 3/4. AC → NC = 1/4.AC. Từ B hạ BH vuông góc AC
Nối BN ta có S∆BNC = 1/2 .NC.BH = 1/2. 1/4.AC.BH
1/4. 1/2 .AC.BH = 1/4.S∆ABC → S∆BNA = 3/4.S∆ABC
từ N hạ NK vuông góc AB ta có AM = 2/3 AB→ MB = 1/3.AB
S∆BNM = 1/2 .NK.BM= 1/2 .NK.1/3AB = 1/3. S∆BNA
→ S∆BNM = 1/3 . 3/4.S∆ABC = 1/4 S∆ABC
Diện tích tứ giác BMNC = S → S = S∆BNC+S∆BNM =120 cm²
→1/4.S∆ABC + 1/4.S∆ABC = 1/2.S∆ABC = 120 cm²
→ S∆ABC = 240 cm²
vẽ hình ra ta sẽ thấy M là trung điểm của AC , N là trung điểm của BC
suy ra từ hình thì ta thấy I bằng N nên bằng nửa BC , M là nửa AC . nên diện tích tam giác AIM bằng 1/4 diện tích ABC :
diện tích AIM là :
600 : 4 = 150 ( cm2)
còn nếu không bạn suy ra từng bước
diện tích 600 cm2 , biết I bằng nửa BC nên chia 2 bằng 300 cm2 , ta lại biết M bằng nửa AC nên lại chia 2 và ra kết quả là 150 cm2
ĐS:...
k mình nhaa ! ^ ^
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