Question

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請問這題怎麼解

如圖,G為△ABC的重心,AD=12,BE=15,
CF=9,求△ABC的面積為?
A
F
E
G
B
C
D
(A) 72
(B) 66
(C) 60
(D) 54

Answer 1

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Mer

延長GD使DH = GD = 4
則BHCG為平行四邊形(因為BD = DC且GD = DH)
BH = GC = 6，△BHG三邊長6,8,10為直角三角形
△BHG = 6*8/2 = 24
△BDG = (1/2)△BHG = 12(因為GD = DH且同高)
△ABC = 6△BDG = 72