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Question
In the figure, if E is the mid-point of median AD, then prove that:
Area (ΔABE) = `1/4` Area (ΔABC).
Sum
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Solution
AD is the median of ΔABC.
Therefore it will divide ΔABC into two triangles of equal areas.
∴ Area(ΔABD) = Area(ΔACD)
Area (ΔABD) = `1/2`Area(ΔABC) ...(i)
In ΔABD, E is the mid-point of AD.
Therefore BE is the median.
∴ Area(ΔBED) = Area(ΔABE)
Area(ΔBED) = `1/2` Area(ΔABD)
Area(ΔBED) = `1/2 xx 1/2`Area(ΔABC) ...[From equation (i)]
Area(ΔBED) = `1/4` Area(ΔABC)
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Triangles with the Same Vertex and Bases Along the Same Line
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