I. The picture represents a hippo pool surrounded by a park.
The two pentagons are similar with AB = 3 CD and the area
of the park is 2,700sq. m Find the area of the pool?

Given that the two pentagons are similar figures, the area of the pool = 675 sq. m..

If two figures are similar to each other, then, the ratio of the square of their corresponding sides equals the ratio of their areas.

We are given that the pool and the park are similar to each other. The diagram given is missing, however, here's how to find the area of the pool:

If x is a side of the pool and y is the corresponding side length of the park, therefore:

area of pool/area of park = x²/y².

Plug in the values given, cross multiply and find the area of the pool.

For example, if 3 is a side of the pool = x

6 is corresponding side of the park = y

Area of park = 2,700 sq. m

Thus:

Area of pool/2,700 = 3²/6²

Area of pool/2,700 = 9/36

Area of pool = (9 × 2,700)/36

Area of pool = 675 sq. m.

Learn more about the areas of similar figure on: