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Question

# In the given figure, AF is parallel to CD, ED is parallel to FC and AD is parallel to BI. J is the mid point of AI. What will be the ratio of Area of trapezium AJCBArea of parallelogram EFCD?

A

1

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B

12

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C

25

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D

34

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Solution

## The correct option is D 34 Fron the given figure, AF is parallel to CD, ED is parallel to FC, and BI is parallel to AD. ABCD and EFCD are parallelograms with the same base CD and between same parallels AF and CD. Thus, area of parallelogram ABCD = area of parallelogram EFCD ------------- (1) △AID and parallelogram ABCD lie on the same base AD and between the same parallels AD and BI Hence, Area of △ AID=12×Area of parallelogram ABCD Now, J is the mid point of AI Hence, DJ is a median of △AID Thus, area of △ADJ = area of triangleAIJ = 12×Area of △AID Thus, area of △ADJ = 14Area of paralleogram ABCD Now, area of trapezium AJCB + Area of △ADJ = Area of parallelogram ABCD Area of trapezium AJCB + 14Area of paralleogram ABCD = Area of parallelogram ABCD Area of trapezium AJCB = 34 Area of paralleogram ABCD} From (1), we have area of parallelogram ABCD = area of parallelogram EFCD Thus, Area of trapezium AJCB = 34 Area of paralleogram EFCD Or, Area of trapezium AJCBArea of parallelogram EFCD=34

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