Find the area of a regular hexagon with the given measurement. 48-inch perimeter

inches

Step-by-step explanation:

Here we are going to use the formula which is

Area=

Where P is perimeter and A is apothem

Here we are given that the Perimeter is 48 inches: Where perimeter is givenas

P=6s

Where s is the side of the hexagon  

6s=48

s=8 inches

Please refer to the image attached with this :

In a Hexagon , there are six equilateral triangle being formed by the three diagonals which meet at point O.  

Consider one of them , 0PQ  with side "s"  

As Apothem is the Altitude from point of intersection of diagonals to one of the side. Hence it divides the side in two equal parts . hence  

Also OP= s

Using Pythagoras theorem ,  

Hence We have Apothem

also we have the perimeter as 48

Now we put them in the main formula  

Area =

Area=

Area=

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)