Question

What is the apothem of a regular hexagon of area 150 square root 3 units?

Answer 1

10 units

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Use formula for the area of a regular hexagon.

• 
  `A = (3/2)*s*a`

where, s - is side and a - is the apothem

There is relationship between the length of the side and the apothem that is specific to regular hexagons:

• 
  `s = a * √(3)`

We can use this relationship to eliminate s in the area formula, giving us:

• 
  `A = (3/2) * a*√(3) * a`

• 
  `A = (3/2) * a^2*√(3)`

The area of the hexagon is given, we equate the values to find the apothem:

• 
  `150*√(3) = (3/2) * a^2 * √(3)`

After cancelling the
`√(3)` from both sides, we simplify the formula to:

• 
  `150 = (3/2) * a^2`

• 
  `a^2 = 150 * (2 / 3)`

• 
  `a^2=100`

• 
  `a=10`

So the apothem is 10 units.