Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
The apothem (x) is 11.62 units, the radius of the circle is 12 units, and the area of each segment is 48π − 23.25√3 square units.
What is a circle?
It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
An equilateral triangle with side lengths equal to 12√3 units is inscribed in a circle.
And half a side length of the equilateral triangle is 6√3 units.
The apothem (x) is units long and the radius of the circle will be
x² = (9√3)² - (6√3)²
x² = 243 - 108
x² = 135
x = 11.62
And the radius of the circle will be
[tex]\begin{aligned} \cos 30 &= \dfrac{6\sqrt3}{r}\\\\\dfrac{\sqrt3}{2}&= \dfrac{6\sqrt3}{r}\\\\r &= 12 \end{aligned}[/tex]
Each segment of the circle has an area that will be
Area = the difference between the areas of the sector and triangle
Area = the areas of the sector - the areas of the triangle
The area of the sector will be
[tex]\rm Sector's \ area= \dfrac{120}{360} \pi *12^2 \\\\Sector's \ area= 48\pi[/tex]
The area of the triangle will be
[tex]\rm Triangle's \ area = \dfrac{1}{2*3} * 11.62 * 12\sqrt3\\\\Triangle's \ area = 23.25\sqrt3[/tex]
Then the area of each segment will be
Segment area = 48π − 23.25√3
More about the circle link is given below.
https://brainly.com/question/11833983
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
