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 (side of the smaller pentagon)
10 m (side of the larger pentagon)
(1 point)
187.5 m²
48 m²
752^2
133 m²
The ratio of the sides of the larger pentagon to the smaller pentagon is 10/4 = 5/2. Since area is proportional to the square of the sides, the ratio of the areas of the larger pentagon to the smaller pentagon is (5/2)^2 = 25/4.
If the area of the smaller pentagon is 30 m², then the area of the larger pentagon is:
(25/4) * 30 = 187.5 m²
Therefore, the area of the larger pentagon is 187.5 m².