Question

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

Answer 1

Answer:

Option (3)

Step-by-step explanation:

Perimeter of a regular hexagon = 30 units

Length of one side = $\frac{30}{6}$

                                = 5 units

Interior angle of hexagon = $\frac{(n-2)\times 180}{n}$

                                           = $\frac{(6-2)\times 180}{6}$

                                           = 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.