Fill in the blanks to make the statements true.

In Fig. 9.25, area of parallelogram BCEF is ________cm² where ACDF is a rectangle.

We know,

Area of parallelogram = Base × Height

Clearly, Height of parallelogram BCEF = CD

Area of parallelogram BCEF = EF × CD

Since BCEF is a parallelogram,

BC = EF [Opposite sides of a parallelogram are equal]… [Eq 1]

Also, ACDF is a rectangle

AC = FD [Opposite sides of a rectangle are equal]… [Eq 2]

Subtracting Eq 1 from Eq 2, we get

AC – BC = FD – EF

⇒ AB = ED

⇒ ED = 3 cm [∵ AB = 3 cm]

Also,

EF = FD – ED

⇒ EF = 10 cm – 3 cm = 7 cm [∵ FD = 10 cm]

Therefore,

Area of parallelogram BCEF

= EF × CD

= 7 cm × 5 cm [∵ CD = 5 cm]

= 35 cm²