The perimeters of two similar polygons are 3: 4. The area of the larger polygon is 56. Find the area of the smaller polygon.

We are given that the perimeters of two similar polygons are related as 3: 4, hence the coefficient of similarity is k.

The area ratio is equal to the square of the similarity coefficient, therefore the area ratio will be: 0.75 * 0.75 = 0.5625;

Now that we know the area ratio, we can find the area of the second triangle, it will be equal to:

56 * 0.5625 = 31.5;

Answer: The area of the smaller triangle is 31.5.