Assume there are 2 similar polygons, whose scale factor is 4:5. If the larger polygon has an area of 30 units squared, what is the area o the smaller polygon?
Areas of similar triangles are proportional to the square of their corresponding sides.
area of smaller/area of larger = 4^2/5^2
area of smaller /30 = 16/25
area of smaller = 30(16/25) = 96/5 or 19.2
To find the area of the smaller polygon, we need to determine the scale factor between the two polygons. In this case, the scale factor is given as 4:5. This means that every length or area measurement on the larger polygon is 4 units, while on the smaller polygon it is 5 units.
Since the area of the larger polygon is given as 30 units squared, we can use this information to find the ratio of areas between the two polygons.
To find the ratio of areas, we square the scale factor: (4^2)/(5^2) = 16/25.
Now, we can find the area of the smaller polygon by multiplying the ratio of areas by the area of the larger polygon: (16/25) * 30 = 19.2 units squared.
Therefore, the area of the smaller polygon is 19.2 units squared.