1. Doubling, tripling, or quadrupling the number of polygons will also double, triple or quadruple the perimeter, respectively. This is because the perimeter is simply the sum of the lengths of all the sides, and when the number of sides increases, the total length of the sides also increases in proportion.
2. Doubling, tripling, or quadrupling the number of polygons will increase the area by a factor of four, nine, or sixteen, respectively. This is because the area of a polygon is proportional to the square of its length, so when the number of sides increases, the area increases faster due to the squared effect.
3. If the ratio of side lengths for two similar pentagons is 1/5, then you would expect the ratio of the perimeters to be 1/5 as well. This is because similar polygons have proportional side lengths, so the ratio of their perimeters will simply be the same as the ratio of their corresponding side lengths.
4. If the ratio of side lengths for two similar pentagons is 1/5, then you would expect the ratio of the areas to be (1/5)^2, or 1/25. This is because the area of a polygon is proportional to the square of its side length, so if you decrease the side length by a factor of 1/5, the area will decrease by a factor of (1/5)^2.
1.)How does doubling, tripling, quadrupling polygons affect the perimeter?
2. How does doubling, tripling, quadrupling polygons affect the area?
3.) If the ratio of side lengths for two similar pentagons is ⅕ , what do you expect the ratio of the perimeters to be?
4.) If the ratio of side lengths for two similar pentagons is ⅕, what do you expect the ratio of the areas to be?
Thank you.
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