Answered

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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

Sagot :

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:

[tex]P_h = 6x[/tex]

Area of a regular hexagon:

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

[tex]A_h = \frac{3\sqrt{3}x^{2}}{2}[/tex]

It has a perimeter of 45 units.

This means that:

[tex]6x = 45[/tex]

[tex]x = \frac{45}{6}[/tex]

[tex]x = 7.5[/tex]

What is the are of the deck

[tex]A_h = \frac{3\sqrt{3}x^{2}}{2} = \frac{3\sqrt{3}*(7.5)^{2}}{2} = 146.14[/tex]

The area of the deck is of 146.14 squared units.

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