Question

the figure shows a parallelogram abcd where ab=10cm and bc=6cm.if de=9cm, find the ,
1. Area ,
2.perimeter,
Of the parallelogram

Answer 1

Answer:

Given−

ABCDisaparallelogramwithAEForAFasthebisectorof

∠A.BCproducedmeetAFatF.AB=10cm,AD=6cm.

Tofindout−

ThelengthofCF=?

Solution−

AEisthebisectorof∠BAD

∴∠BAE=∠DAE.......(i)

ButAB∥DC(ABCDisaparallelogram)

∴∠BAE=∠DEA(altangles)

∠DAE=∠DEA(fromi)

∴ΔDAEisisosceles.⟹AD=DE=6cm⟹CE=DC−DE=(10−6)cm=4cm

AlsoAB=DC=10cm&AD=BC=6cm.(oppositesidesofaparallelogram).......(ii)

NowbetweenΔAFB&ΔEFCwehave

∠BAF=∠CEF&∠ABF=∠ECF(correspondingangles)

and∠AFBor∠EFCiscommon.

∴ΔAFB&ΔEFCaresimilar.

∴

CF

BF

=

EC

AB

⟹

CF

BC+CF

=

4

10

⟹

CF

BC

+1=

4

10

CF

6

+1=

4

10

⟹CF=4cm

Ans−CF=4cm

solution