Understanding Regular Triangles

What is a defining characteristic of a regular triangle?

• It has one right angle.

• All sides and angles are congruent.

• All sides are different lengths.

• It has two equal sides.

What is the role of the apothem in a regular polygon?

• It forms a 90-degree angle with a side.

• It bisects the central angle.

• It is equal to the radius.

• It connects two vertices.

How is the central angle of a regular triangle calculated?

• 180 degrees divided by the number of sides.

• 360 degrees divided by the number of sides.

• The sum of all interior angles.

• The difference between two interior angles.

In a 30-60-90 triangle, what is the relationship between the sides?

• All sides are equal.

• The side opposite 90 degrees is twice the side opposite 30 degrees.

• The side opposite 60 degrees is twice the side opposite 30 degrees.

• The side opposite 30 degrees is twice the side opposite 60 degrees.

If a regular triangle has a perimeter of 30 inches, what is the length of each side?

• 5 inches

• 20 inches

• 10 inches

• 15 inches

Given a regular triangle with a perimeter of 30 inches, what is the apothem length?

• 10 inches

• 7.5 inches

• 5 inches

• 2.9 inches

For a regular triangle with a perimeter of 30 inches, what is the calculated area?

• 60 square inches

• 50 square inches

• 43.5 square inches

• 30 square inches

If a regular triangle has a radius of 12 cm, what is the apothem length?

• 12 cm

• 9 cm

• 6 cm

• 3 cm

For a regular triangle with a radius of 12 cm, what is the side length?

• 25 cm

• 20.8 cm

• 15 cm

• 10.4 cm

What is the area of a regular triangle with a radius of 12 cm?

• 100 cm²

• 87.2 cm²

• 62.4 cm²

• 120 cm²