73.6k views
15 votes
Does anybody know this?The two pentagons shown are similar if the area of the smaller pentagon is 232m^3 find the area of the larger pentagon

Does anybody know this?The two pentagons shown are similar if the area of the smaller-example-1

1 Answer

10 votes

Answer:

(a) 362.5 m²

Explanation:

The ratio of areas is proportional to the square of the ratio of side lengths.

__

scale factor

larger/smaller = (35 cm)/(28 cm) = 5/4

area

The larger area is the square of this scale factor times the smaller area.

(5/4)²(232 m²) = 362.5 m²

_____

Additional comment

We assume the units are intended to match. It is impossible for a pentagon with a side length of 28 cm to have an area of 232 m². A regular pentagon with a side length of 28 cm will have an area of about 0.1349 m².

User Tamica
by
4.1k points