A regular pentagon has side length 12 cm. The perimeter of the pentagon is 60 cm and the area is 247.7 cm2. A second pentagon has side lengths equal to 18 cm. Find the area of the second pentagon. Round to the nearest tenth.

Question

directrix · Answer

Any two regular pentagons are similar.

The square of the scale factor of two similar polygons is equal to the ratio of the areas of the two regular polygons.

directrix · Answer

The square of 12 to 18 is the ratio of 247.7 to A where A is the area of the second pentagon.

directrix · Answer

(12/18)^2 = 247.7/A

(2/3)^2 = 247.7/A

4/9 = 247.7/A

Cross Multiply and solve for A.

mathslover · Answer

@kwatts19 , welcome to openstudy