In figure (2) given below, the side AB of the parallelogram ABCD is produced to E. A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is completed. Prove that
area of || gm BFGE = area of || gm ABCD.

Question

In figure (2) given below, the side AB of the parallelogram ABCD is produced to E. A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is completed. Prove that
area of || gm BFGE = area of || gm ABCD.

KnowledgeBoat · Accepted Answer

Join AC and EF. Since, ∆AFC and ∆AFE lie on same base AF and between same parallel lines AF and CE so, area of ∆AFC = area of ∆AFE Now, subtract area of ∆ABF on both sides, area of (∆AFC - ∆ABF) = area of (∆AFE – ∆ABF) area of ∆ABC = area of ∆BEF 2 area of ∆ABC = 2 area of ∆BEF .......(i) From figure, As || gm ABCD and ∆ABC lie on same base AB and between same parallel lines AB and DC. Area of ∆ABC = Area of || gm ABCD Area of || ABCD = 2 Area of ∆ABC .........(ii) As || gm BFGE and ∆BEF lie on same base BE and between same parallel lines FG and BE. Area of ∆BEF = Area of || gm BFGE Area of || BFGE = 2 Area of ∆BEF .........(iii) Substituting value from (ii) and (iii) in (i) we get, Area of || ABCD = Area of || BFGE. Hence, proved that area of || ABCD = area of || BFGE.

Mathematics

In figure (2) given below, the side AB of the parallelogram ABCD is produced to E. A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is completed. Prove that
area of || gm BFGE = area of || gm ABCD.

Theorems on Area

Related Questions

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Mathematics

In figure (2) given below, the side AB of the parallelogram ABCD is produced to E. A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is completed. Prove thatarea of || gm BFGE = area of || gm ABCD.

Theorems on Area

Related Questions

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In the figure (1) given, ABCD and AEFG are two parallelograms. Prove that area of || gm ABCD = area of || gm AEFG.

In figure (2) given below, the side AB of the parallelogram ABCD is produced to E. A straight line through A is drawn parallel to CE to meet CB produced at F and parallelogram BFGE is completed. Prove that
area of || gm BFGE = area of || gm ABCD.