Question

prove that the areas of parallelogram ABCD and rectangle ABEF standing on same base AB and between the same parallel lines AB and PQ are equal.​

Answer 1

Given :- prove that the areas of parallelogram ABCD and rectangle ABEF standing on same base AB and between the same parallel lines AB and FC are equal.

Answer :-

we know that,

• Area of rectangle = Length * Breadth.
• Area of parallelogram = Base * perpendicular height .

from image we have,

• ABEF is a rectangle .
• ABCD is a parallelogram .

so,

→ Area of rectangle ABEF = L * B = AB * EB ---------- Eqn.(1)

and,

→ Area of parallelogram ABCD = Base * perpendicular height = AB * BE = AB * EB ---------- Eqn.(2)

from Eqn.(1) and Eqn.(2) ,

→ AB * EB = AB * EB

therefore,

→ Area of rectangle ABEF = Area of parallelogram ABCD .

Hence, the areas of parallelogram ABCD and rectangle ABEF standing on same base and between same parallel lines have equal area .

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