The ratio of the area of the smaller triangle to the area of the bigger triangle is 1:4

. When two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides

. In this case, the sides of the larger triangle are twice the length of the sides of the smaller triangle. So the ratio of the sides is 1:2. Squaring this ratio gives the ratio of the areas, which is $$1^2 : 2^2$$ = 1:4

. For similar triangles $$\Delta ABC$$ and $$\Delta DEF$$, the area ratio can be expressed as $$ \frac{\text{Area of } \Delta ABC}{\text{Area of } \Delta DEF} = \frac{(AB)^2}{(DE)^2} = \frac{(BC)^2}{(EF)^2} = \frac{(AC)^2}{(DF)^2} $$