In the given figure, the sides YX, XZ, ZY are extended such that MY=YZ, NX=XY, XZ=ZO. The area of XYZ = 10, what is the area of DMNO ___

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Solution

In the given figure, let’s join Y to O, Z to N and X to M.

Consider DMNY, since MX is a median, area ofD MXN = area of DMXY.

But, area of DMXY = area of DXZY (XY is a median). Thus area of DMXN=area of DXZY

This is continued for all the smaller triangles formed, hence DMNO = 7D XZY.

Thus area of DMNO = 70.

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