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?
Ratio of area between similar figures
= (ratio of linear dimensions)²
For the given polygons,
linear ratio = 8/7
area ratio = (8/7)²
Can you take it from here?
no i knew that part its the rest
So if the smaller one is 512 m², and the ratio is (8/7)², what is the area of the larger polygon? Post what you get.
342m^2
To find the area of the larger figure, we need to use the fact that the ratio of corresponding sides is 8:7.
Since the ratio of corresponding sides is 8:7, we can assume that every linear dimension (length, width, height) of the smaller figure is multiplied by 8/7 to get the corresponding dimension of the larger figure.
The ratio of any two corresponding linear dimensions is equal to the ratio of their respective areas. Since the ratio of the dimensions is 8:7, the ratio of their areas will be (8/7)^2 = 64/49.
This means that the area of the larger figure is (64/49) times the area of the smaller figure.
Given that the area of the smaller figure is 512 square meters, we can calculate the area of the larger figure as follows:
Area of larger figure = (64/49) * Area of smaller figure
= (64/49) * 512
= 665.6 square meters
Therefore, the area of the larger figure is 665.6 square meters.