Answer to Question #158210 in Geometry for Janine Leodones

Question

Given two regu

lar polygons of the same number of sides. If the area of the first is

3 times the area of the second, find the ratio of (a) their perimeters, and (b) their

apothems.

Answer 1

If two regular polygons of the same number of sides are given then such polygons are

similar

$$k=\dfrac{side_1}{sie_2}=\dfrac{perimeter_1}{perimeter_2}=\dfrac{apothem_1}{apothem_2}$$

$$=\sqrt{\dfrac{Area_1}{Area_2}}$$

Given $\dfrac{Area_1}{Area_2}=3$

(a)

$$\dfrac{perimeter_1}{perimeter_2}=\sqrt{3}$$

(b)

$$\dfrac{apothem_1}{apothem_2}=\sqrt{3}$$