Question

I do know that the second box is right, but I am having trouble figuring the rest of it out. Can you help me?

Answer 1

Step-by-step explanation

With the length of the apothem, we can get the length of the side by applying the following relationship:

`a=x√(3)`

Where a represents the apothem and x represents a half of the length of the side.

Plugging in the terms:

`8=x√(3)`

Isolating the value of x:

`x=(8)/(√(3))`

Simplifying:

`x=(8√(3))/(3)\approx4.62`

Now, the side length is equivalent to two times the value of x:

`side\text{ length=s=2x=2*4.6=9.2cm}`

The side length is 9.2cm

c) Therefore, the third statement is not true.

a) Multiplying the side length by 6 give us the perimeter:

`9.2*6=55.2cm`

Therefore, the perimeter is 55.2, not 48cm. The first statement is not true.

d) The fourth statement is true, in a regular hexagon, the radius equals the side length.

e) Area of the hexagon:

The area of the hexagon can be obtained by applying the following equation:

`Area_{regular\text{ hexagon}}=(1)/(2)*Perimeter*apothem`

Plugging in the known terms into the expression:

`Area_{regular\text{ hexagon}}=(1)/(2)*55.2*9.2=253.92`

Since the area is approximately equal to 253.92, the last statement is not true.

In conclusion, the solutions are:

a) NOT TRUE

b) TRUE

c) NOT TRUE

d) TRUE

e) NOT TRUE