老少咸宜,男女俱歡(click 我啦!)maths....2

BCFE面積 =24 cm²
(BH + HC) x FC = 24 cm² ...... (1)

DCHG面積 = (1/4) x ABCD面積
(DF + FC) x HC = (1/4) x (DF + FC) x (BH + HC)
(DF + FC) x 4HC = (DF + FC) x (BH + HC) ...... (2)
4HC = BH + HC
HC = BH/3 ...... (3)

FCHM面積 = (1/6) x ABCD面積
FC x HC = (1/6) x (DF + FC) x (BH + HC)
FC x 6HC = (DF + FC) x (BH + HC) ...... (4)

(2) = (3) :
(DF + FC) x 4HC = FC x 6HC
4DF + 4FC = 6FC
2FC = 4DF
FC = 2DF ...... (5)

(3) 及 (5) 代入(1) :
[BH + (BH/3)) x 2DF = 24 cm²
(4BH/3) x 2DF = 24 cm²
BH x DF = 9 cm²

陰影部分面積
= AG x GM
= BH x DF
= 9 cm²