Area of △DFC → 1/2 x 10 x 9
= 45 cm²

Since area of shaded part EGCD is 5/9 the area of △DFC,

Area of shaded part EGCD → 5/9 x 45
= 25 cm²

Since area of shaded part EGCD is also 5/6 the area of rectangle ABCD,

Area of rectangle ABCD → (25 ÷ 5) x 6
= 30 cm²

Area of rectangle ABCD = Width BC x Length CD
30 cm² = BC x 10 cm
BC = 3 cm

Thank you very much