XD is a median of triangle XYZ E is a point on XD such that XE=ED find area of - Maths - Areas of Parallelograms and Triangles

Question

XD is a median of triangle XYZ E is a point on XD such that XE=ED
find area of triangle YXD: area of triangle XEZ

Manbar Singh · Accepted Answer

We know that, a median of a ∆ divides it into 2 ∆'s of equal areas
Since, XD is a median to side YZ of ∆XYZ, thenar∆YXD = ar∆ZXD = 12ar∆XYZ    
1⇒ar∆YXD =  12ar∆XYZ    Now, we have XE = ED, soZE is a median to side XD of ∆ZXD
Now, we know that, a median of a ∆ divides it into 2 ∆'s of equal areas
So, ar∆XEZ = ar∆DEZ = 12ar∆ZXD⇒ ar∆XEZ = 12ar∆ZXD⇒ ar∆XEZ = 12×12ar∆XYZ   Using 1⇒ar∆XEZ = 14ar∆XYZNow, ar∆YXDar∆XEZ = 12ar∆XYZ14ar∆XYZ = 21

XD is a median of triangle XYZ. E is a point on XD such that XE=ED find area of triangle YXD: area of triangle XEZ