Question

The Gomez’s deck is shown below. The deck is a regular hexagon. It has a perimeter of 45 units. What is the are of the deck

Answer 1

The area of the deck is of 146.14 squared units.

Explanation:

Regular hexagon:

A regular hexagon has 6 sides, all with the same measure.

Perimeter of a regular hexagon:

The perimeter of a regular hexagon with side x is given by:

`P_h = 6x`

Area of a regular hexagon:

The area of a regular hexagon with side x is given by:

`A_h = (3√(3)x^(2))/(2)`

It has a perimeter of 45 units.

This means that:

`6x = 45`

`x = (45)/(6)`

`x = 7.5`

What is the are of the deck

`A_h = (3√(3)x^(2))/(2) = (3√(3)*(7.5)^(2))/(2) = 146.14`

The area of the deck is of 146.14 squared units.