The pentagons below are similar. The area of the smaller pentagon is 30 m². What is the area of the larger pentagon in m²?
4m
10 m
(1 point)
187.5 m²
48 m²
Ο 752
133 m²
Assuming that the side length of the larger pentagon is 4m, we can find the ratio of the sides of the two pentagons.
Let x be the ratio of sides between the larger and smaller pentagon.
x = 4m / 10m
x = 0.4
Since area is proportional to the square of the side length, the ratio of the areas of the two pentagons is x^2.
Ratio of areas = 0.4^2
Ratio of areas = 0.16
Area of the larger pentagon = 30 m² / 0.16
Area of the larger pentagon = 187.5 m²
Therefore, the area of the larger pentagon is 187.5 m².