how do you solve this

Area of a polygon: A=1/2aP
Perimeter: P=ns

It is a hexagon (6 sides) the sides measure 8cm therefore I have a perimeter measuring
P=6(8)=48 RIGHT?
and for the area I have A=1/2 the apothem= 4 square root of 3 and the P= 48
so, A=1/2(4 square root of 3)48, but how do you solve that??

To solve the equation A = 1/2aP for the given values (a = 4√3, P = 48), you can substitute these values into the equation and simplify.

A = 1/2(4√3)(48)

First, simplify the expression inside the parentheses:

A = 1/2(4√3)(48)
= 1/2 * 4 * 48 * √3
= 2 * 48 * √3
= 96√3

So, the area of the hexagon is 96√3 square units.

To solve for the area of the hexagon, you have the formula A = 1/2ap, where "a" represents the apothem (the distance from the center of the polygon to any of its sides), and "p" represents the perimeter of the polygon.

Given that the hexagon has 6 sides measuring 8cm each, you correctly calculated the perimeter: P = 6(8) = 48cm.

To find the apothem "a," you have mentioned that it is equal to 4√3. Now you can substitute the values into the formula:

A = 1/2(4√3)(48)

First, you can simplify 1/2(4√3) as 2√3:

A = 2√3(48)

Next, multiply 2√3 by 48:

A = 96√3

So, the area of the hexagon is 96√3 square centimeters.

To calculate this, you can use a scientific calculator to find the value of the square root of 3 and then multiply it by 96.

your answer of

Area = (1/2)(4√3)(48)
= 96√3
should be an acceptable answer, since it is "exact".

If you want a decimal equivalent, you can use your calculator.