Question

question 1 of 10

there are six equilateral triangles in a regular ______.

a. square
b. polygon
c. octagon
d. hexagon

Explanation:

Analyze regular polygon decomposition

A regular polygon with \(n\) sides can be divided into \(n\) congruent triangles by drawing segments from its center to each of its vertices.

Determine the triangle type

For a regular polygon with \(n\) sides, the central angle of each triangle is:

$$ \theta = \frac{360^\circ}{n} $$

If the triangles are equilateral, the central angle must be \(60^\circ\):

$$ \frac{360^\circ}{n} = 60^\circ \implies n = 6 $$

Identify the polygon

A regular polygon with 6 sides is a regular hexagon. Therefore, there are six equilateral triangles in a regular hexagon.

Answer:

• A. square
• B. polygon
• C. octagon
• D. hexagon (Correct answer)