in the adjoining figure E is midpoint of the side AB of a traingle ABC and EBCF id a parallelogram. if the area of triangle abc is 25 sq. units, find the area of parallelogram ebcf.....
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in the adjoining figure E is midpoint of the side AB of a traingle ABC and EBCF id a parallelogram. if the area of triangle abc is 25 sq. units, find the area of parallelogram ebcf.....
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hey abhi bhai , here is your answer..
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explanations:
Let us consider EF, side of ∥gm BCFE meets AC
at G. We know that,
E is the mid-point and EF∥BC
G is the mid-point of AC.
So, AG=GC
Now, in △AEG and ΔCFG,
The alternate angles are:
∠EAG,∠GCF
Vertically opposite angles are:
∠EGA=∠CGF
So,AG=GC
Proved.
∴ΔAEG≅ΔCFG
ar(ΔAEG)=ar(ΔCFG)
Now,
ar (∥gm EBCF )
=arBCGE+ ar (ΔCFG)
=arctgE+ar(ΔAEG)
=ar(ΔABC)
We know that, ar (ΔABC)=25sq. units
Hence, ar (∥gm EBCF )=25 sq. units
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miss you abhi bro❤❤......
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Let us consider EF, side of ∥gm BCFE meets AC at G. We know that,
E is the mid-point and EF∥BC
G is the mid-point of AC.
So, AG=GC
Now, in △AEG and ΔCFG,
The alternate angles are:
∠EAG,∠GCF
Vertically opposite angles are:
∠EGA=∠CGF
So,AG=GC
Proved.
∴ΔAEG≅ΔCFG
ar(ΔAEG)=ar(ΔCFG)
Now,
ar (∥gm EBCF )
=arBCGE+ ar (ΔCFG)
=arctgE+ar(ΔAEG)
=ar(ΔABC)
We know that, ar (ΔABC)=25sq. units
Hence, ar (∥gm EBCF )=25 sq. units