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

Answer:

The area of the deck is of 146.14 squared units.

Step-by-step 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:

$A_h = \frac{3\sqrt{3}x^{2}}{2}$

It has a perimeter of 45 units.

This means that:

$6x = 45$

$x = \frac{45}{6}$

$x = 7.5$

What is the are of the deck

$A_h = \frac{3\sqrt{3}x^{2}}{2} = \frac{3\sqrt{3}*(7.5)^{2}}{2} = 146.14$

The area of the deck is of 146.14 squared units.