Question

The regular hexagon shown below has a perimeter of 30 and center C. What is the perimeter of triangle ABC.

Answer 1

Option (3)

Explanation:

Perimeter of a regular hexagon = 30 units

Length of one side =
`(30)/(6)`

= 5 units

Interior angle of hexagon =
`((n-2)* 180)/(n)`

=
`((6-2)* 180)/(6)`

= 120°

BC is an bisector of the angle measuring 120°.

m∠ABC = 60°

Similarly, m∠BCA ≅ ∠CAB ≅ 60°

Therefore, ΔABC is an equilateral triangle.

By the property of equilateral triangle, all sides of the triangle will be equal in measure.

AB ≅ BC ≅ AC ≅ 5 units

Perimeter of triangle ABC = AB + BC + AC

= 5 + 5 + 5

= 15 units

Option (3) will be the answer.