In the given figure, if area of triangle ADE is 60 cm²; state, giving reason, the area of :

(i) parallelogram ABED;

(ii) rectangle ABCF;

(iii) triangle ABE.

(i) We know that,

Area of triangle is half that of a parallelogram, on the same base and between the same parallels.

From figure,

△ ADE and parallelogram ABED lies on same base DE and between same parallel lines AB and DE.

∴ Area of △ ADE = $\dfrac{1}{2}$ Area of parallelogram ABED

⇒ Area of parallelogram ABED = 2 × Area of △ ADE

⇒ Area of parallelogram ABED = 2 × 60 = 120 cm².

Hence, area of parallelogram ABED = 120 cm².

(ii) We know that,

Area of parallelogram is equal to area of a rectangle on the same base and between same parallel lines.

From figure,

Parallelogram ABED and rectangle ABCF lie on lie on same base AB and between same parallel lines AB and CD.

∴ Area of rectangle ABCF = Area of parallelogram ABED = 120 cm².

Hence, area of rectangle ABCF = 120 cm².

(iii) We know that,

Area of a triangle is half that of a parallelogram on the same base and between the same parallels.

∴ Area of triangle ABE = $\dfrac{1}{2}$ Area of parallelogram ABED

= $\dfrac{1}{2} \times 120$ = 60 cm².

Hence, area of triangle ABE = 60 cm².