To raise awareness about hazards of smoking, a school decides to start 'NO SMOKING' campaign Students were asked to prepare - Math - Triangles

Question

To raise awareness about hazards of smoking, a school decides to
start 'NO SMOKING' campaign Students were asked to prepare banners
in the shape of triangle as shown in the figure Design of the
banner is such that AD is the median and E is the mid-point AD
a) Show that ar (triangle BED) = 1/4 ar (triangle ABC)
b) Do you think such campaigns should be organized Justify

Manbar Singh · Accepted Answer

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In △ ABC, AD is the median to side BC
We know that the median of a △ divides it into two triangles
of equal areas
So, ar △ ABD = ar △ ACD ⇒ ar △ ABD = 12 ar
△ ABC 1Since E is the mid point of AD, so BE is the median to
side AD of △ ABD Now we know that median of a △ divides
it into two triangles of equal areas, so, ar △ BED = ar
△ AEB⇒ ar △ BED = 12 ar △ ABD 2Putting the
value of ar △ ABD from 1 and 2, we get,ar △ BED = 14 ar
△ ABC

Such type of campaigns should be organised so that people should be
encouraged to stop smoking and stop drinking