Question

The area of the regular hexagon is 169.74 ft2. A regular hexagon has an apothem with length 7 feet and an area of 169.74 feet squared. What is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft

Answer 1

C

Explanation:

edge 2021

Answer 2

Answer:
`48.5\ ft`

Explanation:

Given

Area of the regular hexagon is
`169.74\ ft^2`

Length of the apothem is
`l=7\ ft`

Suppose the side of the hexagon is a

Hexagon can be divided into six equal triangles with same area

Area of a single triangle is

`\Rightarrow A_1=(1)/(2)* 7* a\\\\\Rightarrow A_1=3.5a\ ft^2`

Area of hexagon will be equal to area of 6 equal area triangles

`\Rightarrow 6A_1=169.74\\\Rightarrow 6* 3.5a=169.74\\\Rightarrow a=8.08\ ft`

Perimeter of the hexagon is

`\Rightarrow P=6a\\\Rightarrow P=6* 8.08\\\Rightarrow P=48.49\approx 48.5\ ft`

Thus, the perimeter of the hexagon is
`48.5\ ft`