Question

The similarity ratio of two similar polygons is 7:4. find the ratio of their areas.

a. 4:1
b. 7:4
c. 4:8
d. 49:16

Answer 1

(d)

Step-by-step explanation:

given 2 similar figures in the ratio a : b , then the

ratio of their areas is a² : b²

given the similarity ratio is 7 : 4 , then

ratio of their areas = 7² : 4² = 49 : 16

Answer 2

The ratio of the areas of two similar polygons with a similarity ratio of 7:4 is 49:16 because the ratio of areas is the square of the scale factor.

Step-by-step explanation:

The student asked about the ratio of the areas of two similar polygons with a similarity ratio of 7:4. To find the area ratio, we use the rule that states that the ratio of the areas of similar figures is the square of the scale factor. In this case, squaring the similarity ratio 7:4 gives us 49:16. Therefore, the ratio of their areas is 49:16.

It's important to remember that when comparing areas of similar figures, we always square the scale or similarity ratio. This means if you have a scale factor of a:b for the dimensions, the scale factor for the area will be a2:b2.