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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) 12(ar ABC)

(b) 13(ar ABC)

(c) 14(ar ABC)

(d) (ar ABC)


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
ar(AFDE)=ar(△AFE)+ar(△FED)
=2ar(△AFE)=
=2×1 fourthar(△ABC)=1 halfar(△ABC)
Hence, the correct answer is option (a). 


Mathematics
Secondary School Mathematics IX
Standard IX

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