Two similar hexagons corresponding sides 2cm and 5 cm.find the ratio of their area, find the area of the larger hexagon is 150cm².find the area of smaller one
The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding sides.
Let the side lengths of the larger hexagon be 5 cm and the side lengths of the smaller hexagon be 2 cm. The ratio of their side lengths is 5/2 = 2.5.
The ratio of their areas is 2.5^2 = 6.25.
Given that the area of the larger hexagon is 150 cm², we can find the area of the smaller hexagon as follows:
Area of smaller hexagon = Area of larger hexagon / 6.25
Area of smaller hexagon = 150 cm² / 6.25
Area of smaller hexagon = 24 cm²
Therefore, the area of the smaller hexagon is 24 cm².