The pentagons below are similar. The area of the smaller pentagon is 30 m^2. What is the area of the larger pentagon.
The picture shows the smaller pentagon with the side = 4
and the larger pentagon with the side = 12
Since the pentagons are similar, their corresponding sides are proportional.
The ratio of the corresponding sides of the larger pentagon to the smaller pentagon is 12/4 = 3.
Therefore, the ratio of their areas is (3)^2 = 9.
If the area of the smaller pentagon is 30 m^2, then the area of the larger pentagon is:
30 x 9 = 270 m^2.
So the area of the larger pentagon is 270 m^2.