C A B D E M N P Q I F A G H K

+) MB // FG

Mà AB = \(\dfrac{1}{4}\) AF  => MB = \(\dfrac{1}{4}\) FG = \(\dfrac{1}{4}\) BC => CM = \(\dfrac{3}{4}\) BC

S_ACM = \(\dfrac{1}{2}\).h.CM = \(\dfrac{1}{2}\).h.\(\dfrac{3}{4}\) BC = \(\dfrac{3}{4}\) S_ABC = \(\dfrac{3}{4}\) . 6 = \(\dfrac{9}{2}\)

+) KN // AC 

Mà GK = \(\dfrac{2}{3}\) CG (1)  => KN = \(\dfrac{2}{3}\) AC

KP // CM (2)

Từ (1) và (2) => KP = \(\dfrac{2}{3}\) CM

S_KNP = \(\dfrac{1}{2}\)sin60^o.KN.KP = \(\dfrac{1}{2}\)sin60^o.\(\dfrac{2}{3}\)AC.\(\dfrac{2}{3}\)CM = \(\dfrac{4}{9}\) S_ACM = \(\dfrac{4}{9}\).\(\dfrac{9}{2}\) = 2

+) HI // CM

Mà HG = \(\dfrac{1}{3}\) CG (3)  => HI = \(\dfrac{1}{3}\) CM

HQ // AC (4)

Từ (3) và (4) => HQ = \(\dfrac{1}{3}\) AC

S_HQI = \(\dfrac{1}{2}\)sin60^o.HI.HQ = \(\dfrac{1}{2}\)sin60^o.\(\dfrac{1}{3}\)CM.\(\dfrac{1}{3}\)AC = \(\dfrac{1}{9}\)S_ACM = \(\dfrac{1}{9}\).\(\dfrac{9}{2}\) = \(\dfrac{1}{2}\)

=> S_ACM + S_KNP + S_HQI = \(\dfrac{9}{2}\) + 2 + \(\dfrac{1}{2}\) = 7.