This Quadrilateral Makes Me Crazy!

Geometry Level 2

ABCD is any quadrilateral. M and N are the mid points of sides AB and BC respectively such that Ar(MBND)=4. Find the value of Ar(ABCD).


The answer is 8.

Kushagra Sahni by Kushagra Sahni , 21, India

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1 solution

Marta Reece
Apr 27, 2017

Triangles B D N BDN and N D C NDC have the same area, because they have the same base, N N being a midpoint, and the same height above it, since they share point D D .

Likewise triangles B D M BDM and M D A MDA .

So the area inside B N D M BNDM is exactly one half of the overall area, and area of A B C D ABCD is 4 × 2 = 8 4\times2=\boxed{8} .

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