We were told that triangle XAR is similar to triangle MNT. This means that the ratio of their corresponding sides is equal. This means that the ratio of the their areas is also equal.. Looking at the triangles, NT corresponds to AR. Ratio of corresponding sides is
12/8 = 1.5
This means that the ratio of their areas is also 1.5
If the area of XAR is x and the area of MNT is 36, then
x/36 = 1.5
x = 1.5 * 36
x = 54
The area of XAR is 54
