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

The perimeter of the hexagon is the sum of its side lengths

The perimeter of the hexagon is 48.5 ft

The given parameters are:

$\mathbf{Area = 169.74}$ --- the area of the hexagon

$\mathbf{a = 7}$ -- the apothem

Let the perimeter of the hexagon be p.

So, the area is calculated as:

$\mathbf{Area = \frac 12 pa}$

Substitute values for Area and (a)

$\mathbf{169.74 = \frac 12 \times p \times 7}$

Multiply both sides by 2

$\mathbf{339.48= p \times 7}$

Divide both sides by 7

$\mathbf{48.5= p }$

Rewrite as:

$\mathbf{p = 48.5}$

Hence, the perimeter of the hexagon is 48.5 ft

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