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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) 12ar ABC
(b) 13ar ABC
(c) 14ar ABC
(d) arABC


Solution



(a) 12 ( ar ∆ ABC)

Join, FE.
ABC has been divided into 4 triangles of equal areas. 
So, ​ar(∆AFE) = 14​× ​(ar∆ABC)
∴ ar(∣​∣gm AFDE) = ar (∆AFE) + ar(∆FED)
                            =  2 × ​ar(∆AFE) = ​2 × ​14​ × ​(ar∆ABC) = ​12(ar∆ABC)
Hence, ​ar(∣​∣gm AFDE) = ​​12(ar∆ABC)

Mathematics
RS Aggarwal (2017)
Standard IX

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