Two corresponding sides of similar polygons are in the ratio of 2 : 7. If the area of the smaller figure is 8 square meters, what is the area of the larger figure?
the areas of similar figures are proportional to the square of their corresponding sides.
so 8/x = 2^2/7^2
8/x = 4/49
etc
Cool, thanks!
To find the area of the larger figure, we need to use the ratio of the corresponding sides.
In this case, the ratio of the corresponding sides is 2 : 7.
Since area is proportional to the square of the side length, the ratio of the areas will be the square of the ratio of the sides.
So, to find the area of the larger figure, we need to square the ratio of the sides and multiply it by the area of the smaller figure.
The ratio of the sides is 2 : 7, so the squared ratio is (2/7)^2 = 4/49.
Now, multiply the squared ratio by the area of the smaller figure:
Area of the larger figure = (4/49) * 8 = 32/49 square meters.
Therefore, the area of the larger figure is 32/49 square meters.