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 $c{m}^2$

(i) D, E and F are mid points of BC, CA and AB respectively

(ii) $\therefore \begin{array}{c}\text{FE}||\text{BC and FE}=\frac{1}{2}\text{BC}\\ \text{ED}||\text{AB and ED}=\frac{1}{2}\text{AB}\\ \text{DF}||\text{AC and DF}=\frac{1}{2}\text{AC}\end{array}\}$ mid-point Theorem

(iii) $\therefore$ BDEF, DCEF and DFAC are || gms
(one pair of opposite sides are equal and ||)

(iv) We know diagonal divides a ||gm into two $\Delta$'s of equal area

$\therefore$ area $\Delta BDF$ = area $\Delta DEC$ = area $\Delta AEF$= area $\Delta DEF$
$=\frac{1}{4}\text{area}\Delta ABC=\frac{1}{4}\left(32\right)=8c{m}^2$

$\therefore$ area trapezium BFEC = 3 (area $\Delta BDF$)
$=3\left(8\right)=24c{m}^2$