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Jody wants to cover her regular hexagon shaped table with a protective tablecloth.  In order to do buy a perfectly-fit tablecloth she must know the area of the table.  Using the given measure below, determine the remaining information.  

Side Length: 12 cm

Apothem: 6√3 cm

 

WHats the area? and whats the permiter?

 Jun 19, 2019

Best Answer 

 #2
avatar+4296 
+2

Let's see if I can attack both of the questions.

(a): The area of a regular hexagon can be found by splitting the hexagon into six equilateral triangles, using 30-60-90 triangles by drawing an altitude and multiply this results by six to get the area answer. However, a very popular formula for a hexagon is \(\frac{3\sqrt{3}}{2}s^2\) where \(s\) is the side length of the hexagon, and we will get an area(answer) of \(\boxed{216\sqrt{3}}\) centimeters squared.

 

-We can also solve this first part of the problem by noting the area of a regular figure or shape is half its perimeter times the distance from the center of the polygon to a side. (Try to prove this on your own!) And, the apothem is the distance from the center of a polygon to a side. We can generate and generalize the formula \(\frac{1}{2}*P*A\), where \(P\) is the perimeter and \(A\) is the apothem. Next, the area of the hexagon is \(12*6=72cm\), because the side length of the hexagon is twelve centimeters and a regular hexagon has six equal sides. We have the apothem as \(6\sqrt{3}\) since given in the problem. Thus,l the area is \(\frac{1}{2}*72*6\sqrt{3}=\boxed{216\sqrt{3}}\) centimeters squared. 

 

(b): The perimeter is quite easier than calculating the area since the side length that is given in the problem is twelve centimeters, and a regular hexagon has six equal sides. Thus, the perimeter is \(12*6=72\)centimeters.

 

-tertre

 Jun 19, 2019
 #1
avatar+18439 
+3

A hexagon has 6 sides      each side is 12 cm  so perimeter=    12 * 6 = 72 cm^2

 

Area of hexagon   3sqrt3 /2  * a^2    where a = side length

                              3 sqrt3 144 /2 = 216 sqrt 3   sq cm

 Jun 19, 2019
 #2
avatar+4296 
+2
Best Answer

Let's see if I can attack both of the questions.

(a): The area of a regular hexagon can be found by splitting the hexagon into six equilateral triangles, using 30-60-90 triangles by drawing an altitude and multiply this results by six to get the area answer. However, a very popular formula for a hexagon is \(\frac{3\sqrt{3}}{2}s^2\) where \(s\) is the side length of the hexagon, and we will get an area(answer) of \(\boxed{216\sqrt{3}}\) centimeters squared.

 

-We can also solve this first part of the problem by noting the area of a regular figure or shape is half its perimeter times the distance from the center of the polygon to a side. (Try to prove this on your own!) And, the apothem is the distance from the center of a polygon to a side. We can generate and generalize the formula \(\frac{1}{2}*P*A\), where \(P\) is the perimeter and \(A\) is the apothem. Next, the area of the hexagon is \(12*6=72cm\), because the side length of the hexagon is twelve centimeters and a regular hexagon has six equal sides. We have the apothem as \(6\sqrt{3}\) since given in the problem. Thus,l the area is \(\frac{1}{2}*72*6\sqrt{3}=\boxed{216\sqrt{3}}\) centimeters squared. 

 

(b): The perimeter is quite easier than calculating the area since the side length that is given in the problem is twelve centimeters, and a regular hexagon has six equal sides. Thus, the perimeter is \(12*6=72\)centimeters.

 

-tertre

tertre Jun 19, 2019

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