we dont know any of the angles, or any of the sides

let a be the length BC

let b be the length AC

let c be the length AB

and change ABC to be the opposite angles to a,b,c

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So the area of ABC can be computed in 3 ways, all equal to 24:

Area = 1/2 sin(A)bc

Area = 1/2 sin(B)ac

Area = 1/2 sin(C)ab

The area of XYZ = area of ABC - area of AYX - area of BXZ - area of CYZ

The area of AYX = 1/2 sin(A) (1/3 b)(1/2 c) = 1/2 sin(A) 1/6 (bc). That's 1/6 of the area of ABC, or 4.

Likewise the area of BXZ = 1/2 sin(B) (1/2 c) (1/4 a) = 1/8 of ABC or 3

Area of CYZ = 1/2 sin(C) (2/3 b) (3/4 a) = 1/2 of ABC or 12

So the area of XYZ = 24 - 4 - 3 - 12 = 5

]]>as i said no info about the kind

]]>Point X lies on AB and divide AB into two equal parts. Point Z lies on BC and diviede BC in the ratio: BZ:ZC = 1:3

Point Y lies on AC and divide AC in the ratio: AY:YC=1:2

Find the area of the triangle XYZ

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