Question

1. if a circle has a radius r and an inscribed regular hexagon, what is the perimeter p of the hexagon?

a. p = 12r
b. p = 6r
c. p = 4r
d. p = 3r

1. what must be true for a quadrilateral to be considered a rhombus?

a. all sides are parallel
b. at least two sides are parallel
c. all sides are of equal length
d. diagonals are perpendicular

Explanation:

Step1: Analyze inscribed hexagon

A regular hexagon inscribed in a circle can be divided into six equilateral triangles. The side - length of each equilateral triangle is equal to the radius \(r\) of the circle.

Step2: Calculate hexagon perimeter

Since a regular hexagon has 6 sides and each side has length \(r\), the perimeter \(P = 6r\).

Step3: Recall rhombus definition

A rhombus is defined as a quadrilateral with all sides of equal length.

Answer:

1. b. \(P = 6r\)
2. c. All sides are of equal length