The scale factor of two similar polygons is given.
Find the ratio of their perimeters and the ratio of their areas.
1:6
More data needed.
Well, if the scale factor between the two polygons is 1:6, then it means that one polygon is 1/6th the size of the other. So, let's call the larger polygon "Biggie" and the smaller polygon "Smalls".
For the ratio of their perimeters, we know that the scale factor is 1:6. Since the perimeters are the lengths of the boundaries of the polygons, the ratio of their perimeters would also be 1:6. So, for every 1 unit of perimeter in Biggie, Smalls would have only 1/6th unit of perimeter.
Now, let's move on to the ratio of their areas. Since area is a two-dimensional measurement, the ratio between the areas of two similar polygons is equal to the square of the scale factor. In this case, the scale factor is 1:6, so the ratio of their areas would be (1/6)^2, which is equal to 1:36. So, for every 1 square unit of area in Biggie, Smalls would have only 1/36th of a square unit of area.
So, the ratio of their perimeters is 1:6, and the ratio of their areas is 1:36. But hey, don't worry! Just because Smalls may be smaller, it doesn't mean it can't pack a punch!
To find the ratio of the perimeters of two similar polygons, you simply divide the lengths of their corresponding sides.
In this case, the scale factor is 1:6. This means that for every unit of length in the first polygon, the corresponding length in the second polygon is 6 times larger.
Let's assume the first polygon has a perimeter of P1, and the second polygon has a perimeter of P2.
Since the scale factor is 1:6, the ratio of the perimeters can be expressed as:
P1 : P2 = 1 : 6
To find the ratio of their areas, you need to square the scale factor. This is because the area of a polygon is determined by the square of its lengths. So, the ratio of their areas can be expressed as:
P1 : P2 = (1^2) : (6^2) = 1 : 36
Therefore, the ratio of their perimeters is 1 : 6, and the ratio of their areas is 1 : 36.
To find the ratio of the perimeters of two similar polygons, you simply need to divide the lengths of their corresponding sides. In this case, if the scale factor is 1:6, it means that every side of the smaller polygon is 1/6 of the corresponding side of the larger polygon.
So, if we assume the lengths of the sides of the smaller polygon are a and the lengths of the sides of the larger polygon are b, the ratio of their perimeters would be a/a:b/b.
Simplifying this ratio, we get 1:6. This means that the ratio of the perimeters of two similar polygons with a scale factor of 1:6 is 1:6.
To find the ratio of their areas, you need to square the scale factor. In this case, the scale factor is 1:6, so when you square it, you get (1/6)^2 = 1/36.
This means that the ratio of the areas of two similar polygons with a scale factor of 1:6 is 1:36.