Two corresponding sides of similar polygons are in the ratio of 8:7. If the area of the smaller figure
is 512 square meters, what is the area of the larger figure?
Area is proportional to the square of linear dimensions, for similar figures.
(8/7)^2 * 512 = 668.7 m^2 is the area of the larger similar polygon.
To find the area of the larger figure, we need to know the scale factor between the two polygons. The scale factor represents how much larger or smaller one figure is compared to the other.
In this case, the ratio of the corresponding sides is given as 8:7. To find the scale factor, we divide the larger side length by the smaller side length.
Let's assume the smaller side length is 8x (since the ratio is 8:7) and the larger side length is 7x (since 7 is the smaller side length in the 8:7 ratio).
Now, we can find the area of the larger figure:
The area of a polygon is determined by the square of its side length. So, if the smaller side length is 8x, the area of the smaller figure is (8x)^2 = 64x^2.
We're also given that the area of the smaller figure is 512 square meters. So, we can set up the equation:
64x^2 = 512
To solve for x, we divide both sides of the equation by 64:
x^2 = 512/64
x^2 = 8
Taking the square root of both sides, we get:
x = √8
Since x represents the scale factor, we need to square it to find the area scaling factor:
x^2 = (√8)^2
x^2 = 8
So, the area scaling factor is 8.
Now, to find the area of the larger figure, we multiply the area of the smaller figure by the scaling factor:
Area of larger figure = Area of smaller figure * Scaling factor
Area of larger figure = 512 * 8 = 4096 square meters.
Therefore, the area of the larger figure is 4096 square meters.