Question

which figure has a greater perimeter? 44.8 in 44.8 in 44.8 in 44.8 in 44.8 in 44.8 in 66.8 in 66.8 in 66.8 in 66.8 in 66.8 in 66.8 in

Explanation:

Step1: Calculate perimeter of hexagon

A regular hexagon has 6 equal - sided lengths. Given side length $a = 44.8$ in. The perimeter $P_1$ of a regular hexagon is $P_1=6a$. So, $P_1 = 6\times44.8=268.8$ in.

Step2: Calculate perimeter of pentagon

A regular pentagon has 5 equal - sided lengths. Given side length $b = 66.8$ in. The perimeter $P_2$ of a regular pentagon is $P_2 = 5b$. So, $P_2=5\times66.8 = 334$ in.

Step3: Compare perimeters

Since $268.8<334$, the pentagon has a greater perimeter.

Answer:

The pentagon