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Question

The midpoints of the sides of a triangle along with any of the vertices as the fourth point makes a parallelogram of area equal to
(a) 12arABC
(b) 13arABC
(c) 14arABC


Solution


D, E and F are the midpoints of sides BC, AC and AB respectively. 
On joining FE, we divide ABC into 4 triangles of equal area.
Also, median of a triangle divides it into two triangles with equal area
arAFDE=arAFE+arFED=2arAFE=2×14arABC=12arABC
Hence, the correct answer is option (a). 

Mathematics
RS Aggarwal (2020, 2021)
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