For a triangle ABC, D. E. F are the mid-points of its sides. If ΔABC = 24 sq. units then ΔDEF is

Property : The line joining the mid points of two sides of a triangle is parallel to the third side and half of it.

=> $$DF = \frac{1}{2}BC$$

=> $$\frac{DF}{BC} = \frac{1}{2}$$

Similarly, $$\frac{DE}{AC} = \frac{1}{2}$$ and $$\frac{EF}{AB} = \frac{1}{2}$$

Hence, $$\triangle$$ ABC $$\sim$$ $$\triangle$$ DEF

Property : The ratio of areas of two similar triangles is equal to the square of ratio of their corresponding sides.

=> $$\frac{ar(\triangle DEF)}{ar(\triangle ABC)} = \frac{DF^2}{BC^2}$$

=> $$\frac{ar(\triangle DEF)}{24} = \frac{1}{4}$$

=> $$ar(\triangle DEF)$$ = 6 sq. units