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 ______

• A. 8 $c{m}^2$
• B. 16 $c{m}^2$
• C. 24 $c{m}^2$
• D. 32 $c{m}^2$

Answer 1

The correct option is C 24 $c{m}^2$

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)
$\therefore$ FE $\parallel BC$ (Midpoint theorem)
$\therefore$ FE $\parallel BD$

Similarly ED $\parallel$ AB and FD $\parallel$ AC
$\therefore$ FEDB, FDEC and FDEA are all parallelograms.

Since a diagonal divides a parallelogram into two congruent triangles, hence
$Area\left(\Delta BFD\right)=Area\left(\Delta EFD\right)=Area\left(\Delta ECD\right)=Area\left(\Delta EFA\right)$
$=\frac{1}{4}Area\left(\Delta ABC\right)=8c{m}^2$

Area(BFEC)
$=Area\left(\Delta BFD\right)+Area\left(\Delta EFD\right)+Area\left(\Delta ECD\right)=24c{m}^2$