Question

1. a construction company is building a gazebo with a regular hexagonal base. the architect specifies that the gazebo should be inscribed in a circular foundation with a diameter of 20 feet. the construction foreman needs to mark the six corner posts. what should be the distance from the center of the foundation to each corner post?

show your work:

Explanation:

Step1: Recall properties of regular hexagon

A regular hexagon inscribed in a circle means the vertices of the hexagon lie on the circle. The distance from the center of the circle to any vertex (corner post) is the radius of the circle.

Step2: Calculate the radius

The diameter of the circular foundation is given as 20 feet. The radius \( r \) of a circle is half of its diameter \( d \), so the formula is \( r=\frac{d}{2} \). Substituting \( d = 20 \) feet, we get \( r=\frac{20}{2}=10 \) feet.

Answer:

The distance from the center of the foundation to each corner post is 10 feet.