The pentagons below are similar. The area of the smaller pentagon is 30 m^2. What is the area of the larger pentagon.

Question

The picture shows the smaller pentagon with the side = 4
and the larger pentagon with the side = 12

Answer 1

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.