Question

The area of the regular hexagon is 10.4 in.2. a regular hexagon has side lengths of 2 inches and an area of 10.4 inches squared. an apothem is shown. what is the measure of the apothem, rounded to the nearest tenth of an inch? 1.3 in. 1.7 in. 2.0 in. 3.4 in.

Answer 1

Answer:

  (b)  1.7 in

Step-by-step explanation:

The area of a regular polygon in terms of perimeter and apothem is given by the formula ...

   A = 1/2Pa

For a hexagon, the perimeter is 6 times the side length, so this becomes ...

  A = 1/2(6s)a = 3sa . . . . . for side length 's' and apothem 'a'

__

Solving for the apothem, we find ...

  a = A/(3s)

For the given values of area and side length the apothem is ...

  a = 10.4/(3·2) = 1.733... ≈ 1.7 . . . inches

The apothem, rounded to tenths, is 1.7 inches.