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

Answer 1

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.