Find the area of a regular hexagon with 8 feet sides

Question

My teacher said my calculator should be in degree mode. An example on how I am supposed to do this question is : 360 / 6 = 60

60 = top of one angle

180 - 60 = 120, 120 / 2 = 60

60 = side angle

Area = 1/2*Base*Height

tan (60) = h (10/2)

h = 5 * tan (60), h = 8.66

A = 1/2 (10) (8.66)

A = 43.3

43.3 * 6 = 259.8

Answer 1

draw a diagram

draw one of the 6 congruent triangles

draw the apothem, the segment from the center to the midpoint of the side

this forms 2 congruent triangles

both triangles are 30-60-90 right triangles

the central angle is 360/6=60°

the apothem bisects this angle also, thus the 30-60-90 right triangle

the side opposite the 30º angle (one of the sides of the hexagon) is half of the hypotenuse

the hypotenuse is 8 feet because half of the side is 4 feet (remember that the side got bisected)

using the Pythagorean Theorem...

a^2+4^2=8^2

a^2+16=64

a^2=64-16

a^2=48

a=√48

a=4√3

the area is equal to 1/2 times the apothem times the perimeter (or you could find the area of one triangle and multiply the answer by 6)

A=(1/2)(4√3)(48)

A=2√3*48

A=96*√3

A=96*1.73205

A=166.277 square feet

Answer 2

A = 3* sqrt(3) * a²

2

substituting the 8ft in for A you should get 166.28 ft^2