Question

An equilateral triangle is inscribed in a circle. An apothem is shown. Lines are drawn from each point to the center point to form radii. The angles between the radii are 120 degrees. The angles between the radii and the sides of the triangle are 30 degrees.

An equilateral triangle with side lengths equal to 12 StartRoot 3 EndRoot units is inscribed in a circle.

Half a side length of the equilateral triangle is 6 StartRoot 3 EndRoot units, so the apothem is
units long and the radius of the circle is
units long.

Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (
π −
StartRoot 3 EndRoot) units2.

Answer 1

Answer: 6, 12, 48, 36

Step-by-step explanation:

An equilateral triangle with side lengths equal to 12 StartRoot 3 EndRoot units is inscribed in a circle.

Half a side length of the equilateral triangle is 6 StartRoot 3 EndRoot units, so the apothem is

✔ 6

units long and the radius of the circle is

✔ 12

units long.

Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or (

✔ 48

π −

✔ 36

StartRoot 3 EndRoot) units2.

Answer 2

6

12

48

36

Explanation:

Hope This Helps! :)