Answered

Connect with knowledgeable individuals and find the best answers at IDNLearn.com. Discover in-depth and reliable answers to all your questions from our knowledgeable community members who are always ready to assist.

Find the area of a regular hexagon with the given measurement
48-inch perimeter
A = sq. in.

Sagot :

MathG33kidn
[tex]Area = \frac{3 \sqrt{3} }{2} s^{2} \\ \\ \frac{48}{6} = 8=s \\ \\ Area =\frac{3 \sqrt{3} }{2} 64 \\ \\ Area =166.28[/tex]

Answer

Area of a regular hexagon is given by:

[tex]A = \frac{3\sqrt{3}}{2}a^2[/tex]            .....[1]

where,

A is the area of a regular hexagon

a is the side of the hexagon.

As per the statement:

Perimeter of a regular hexagon is 48 inch.

Perimeter(P) of a regular hexagon is given by:

[tex]P=6a[/tex]

Substitute the given values we have;

[tex]48 = 6a[/tex]

Divide both sides by 6 we have;

[tex]8 = a[/tex]

or

a = 8 inch.

Substitute the value of a = 8 inches  in [1] we have;

[tex]A = \frac{3\sqrt{3}}{2}(8)^2[/tex]

⇒[tex]A = 3\sqrt{3} \cdot 32 = 96\sqrt{3}[/tex]

Therefore, the area of a regular hexagon is[tex]A = 96\sqrt{3}[/tex] sq. in

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.