Question

Look at the Hexagon below

1.Find the measure of each numbered angle
2.if the apotheosisem is 20
`√(x)`3 find the radius and side
3.FInd the area leave your answer in simpilest radical form

Answer 1

Angle 9: 60°

Angle 10: 30°

Side = radius = 40sqrt(x/3)

Area = [800sqrt(3)]x

Explanation:

Total angle in a hexagon:

(6 - 2) × 180

720

Each interior angle:

720/6 = 120

angle 9 = 120/2 = 60

Angle 10 = 60/2 = 30

sin(60) = 20sqrt(x)/r

r = 20sqrt(x) ÷ sqrt(3)/2

r = 40sqrt(x/3)

Side:

sin(30) = ½s/(40sqrt(x/3))

½s = 20sqrt(x/3)

s = 40sqrt(x/3)

Area = (3sqrt(3))/2 × s²

Area = 3sqrt(3)/2 × 1600x/3

Area = [800sqrt(3)]x