Question

E and F are the points of trisection of the diagonal BD of parallelogram ABCD of area 90 sq. cm. Find Area $\square AECF$

• A. 45 sq. cm
• B. 20 sq. cm
• C. 15 sq. cm
• D. 30 sq. cm

Answer 1

The correct option is D

30 sq. cm

$ar\left(\Delta ABD\right)=\frac{1}{2}\times ar\left(\square ABCD\right)$ = 45 sq. cm. . . . . (Diagonal bisects the area)
$ar\left(\Delta ABE\right)=ar\left(\Delta AEF\right)=ar\left(\Delta AFD\right)$ . . . . (Triangles of equal base & height)
$\therefore ar\left(\Delta AEF\right)=\frac{45}{3}=15sq.cm$
Similarly, $ar\left(\Delta EFC\right)$ = 15 sq. cm
$\therefore ar\left(\square AECF\right)$ = 30 sq. cm.