Find the area of a parallelogram-shaped shaded region. Also, find the area of each triangle. What is the ratio of the area of shaded portion to the remaining area of the rectangle?

Here, AB = 10 cm

AF = 4 cm

FB = 10 cm – 4 cm = 6 cm

Area of the parallelogram = Base × Height = FB × AD = 6 cm × 6 cm = 36 cm²

Hence, the required area of shaded region = 36 cm².

Area ∆DEF = 1/2  × b × h

= 1/2  × AF × AD

= 1/2  × 4 × 6

= 12 cm²

Area ∆BEC =  1/2 × b × h

= 1/2 × GC × BC

= 1/2 × 4 × 6

= 12 cm²

Area of Rectangle ABCD = l × b = 10 cm × 6 cm = 60 cm²

Remaining area of Rectangle = 60 cm² – 36 cm² = 24 cm²

Required Ratio = 36 : 24 = 3 : 2