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


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.

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