We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

Point G is the midpoint of median line XM of triangle XYZ. Point H is the midpoint of line XY, and point T is the intersection of line HM and line YG. Find the area of triangle MTG if [XYZ] =150.


I got some help on this earlier but I'm still in the dark.  Thanks!


Here's the way I set it up, ACG :




Look at  triangle YGM

Note that  G  is the midpoint of XM...so  the height of G  above base YM = the height of YGM  =  (1/2)height of triangle XYZ

And since M is the midpoint of YZ, it is  the base of YGM  =  1/2 base of triangle XYZ

And triangles are to each other as the ratio of their bases and heights

So area of triangle YGM  = (1/2)* (1/2 base of XYZ) * (1/2 height of XYZ) =

(1/4) (1/2 base of XYZ) *(height of XYZ)  

(1/4)area of XYZ  =   1/4 XYZ


Now  ...look at triangle YTM

Since YG is  a median of triangle YXM....then YT  = 2/3  of YG

But....this means that T  is (2/3)  the height above base YM that G is

So...the height of triangle YTM  =  2/3   height of triangle YGM

And they are on the same base 

So...the areas of triangles on the same base are to each other as their heights....so..

Area of triangle YTM  = (2/3)area of triangle YGM  =  (2/3)(1/4)XYZ  = (1/6)XYZ


So....area  of triangle  MTG  = 

Area of triangle YGM - Area of triangle YTM =


(1/4)XYZ - (1/6)XYZ  =

(1/4  - 1/6) XYZ =

(2/24)XYZ  =

(1/12)XYZ =

(1/12)(150)  =

12.5 units^2 



cool cool cool

 Mar 9, 2018
edited by CPhill  Mar 10, 2018

Thanks so much!

AnonymousConfusedGuy  Mar 11, 2018

26 Online Users