Question
ABC is a triangle in which D, E, F are the mid-points of BC, AC and AB respectively. If Area (ΔABC) = 32 cm2, then area of trapezium BFEC is ______ 
Answer: Option C
:
C
Given: In △ABC, D,E and F are midpoints of BC, CA and AB.
Area (ΔABC) = 32 cm2
To find:Area of trapezium BFEC
Consider△ABC,
F and E are midpoints of AB and AC. (given)
∴ FE ∥BC(Midpoint theorem)
∴ FE ∥BD
Similarly ED ∥ ABand FD ∥ AC
∴ FEDB, FDEC and FDEA are all parallelograms.
Since a diagonaldivides a parallelogram into two congruent triangles, hence
Area(ΔBFD)=Area(ΔEFD)=Area(ΔECD)=Area(ΔEFA)
=14Area(ΔABC)=8cm2
Area(BFEC)
=Area(ΔBFD)+Area(ΔEFD)+Area(ΔECD)=24cm2
Was this answer helpful ?
:
C
Given: In △ABC, D,E and F are midpoints of BC, CA and AB.Area (ΔABC) = 32 cm2
To find:Area of trapezium BFEC
Consider△ABC,
F and E are midpoints of AB and AC. (given)
∴ FE ∥BC(Midpoint theorem)
∴ FE ∥BD
Similarly ED ∥ ABand FD ∥ AC
∴ FEDB, FDEC and FDEA are all parallelograms.
Since a diagonaldivides a parallelogram into two congruent triangles, hence
Area(ΔBFD)=Area(ΔEFD)=Area(ΔECD)=Area(ΔEFA)
=14Area(ΔABC)=8cm2
Area(BFEC)
=Area(ΔBFD)+Area(ΔEFD)+Area(ΔECD)=24cm2
Was this answer helpful ?
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