Question

A) What is the perimeter of the regular hexagon shown above?B) What is the area of the regular hexagon shown above?(see attached image)

Answer 1

Remember that

A regular hexagon can be divided into 6 equilateral triangles

the measure of each interior angle in a regular hexagon is 120 degrees

so

see the attached figure to better undesrtand the problem

each equilateral triangle has three equal sides

the length of each side is given and is 12 units

Part A) Perimeter

the perimeter is equal to

P=6(12)=72 units

Part B

Find the area

Find the height of each equilateral triangle

we have

tan(60)=h/6

Remember that

`\tan (60^o)=\sqrt[]{3}`

therefore

`h=6\sqrt[]{3}`

the area of the polygon is

`A=6\cdot\lbrack(1)/(2)\cdot(6\sqrt[]{3})\cdot(12)\rbrack`
`A=216\sqrt[]{3}`

alternate way to find out the value of h

applying Pythagorean Theorem

12^2=6^2+h^2

h^2=12^2-6^2

h^2=108

h=6√3 units