SOLUTION: What is the area of the smaller of the two concentric circles if the side length of the equilateral triangle is 8cm? Image- https://media.discordapp.net/attachments/802751414874

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Question 1175877: What is the area of the smaller of the two concentric circles if the side length of the equilateral triangle is 8cm?
Image- https://media.discordapp.net/attachments/802751414874537995/814628897253621810/wP4nMFfWeYnrAAAAABJRU5ErkJggg.png
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
What is the area of the smaller of the two concentric circles if the side length of the equilateral triangle is 8cm?

let radius of greater circle be R, radius of smaller circle be r, the height of the equilateral triangleh, and the side of the equilateral trianglea
from the given image you can see that radius of greater circle is equal to height R=h of the equilateral triangle, and r=R%2F2=h%2F2

if the side a=8cm, then
h=sqrt%28a%5E2-%28a%2F2%29%5E2%29
h=sqrt%288%5E2-%288%2F2%29%5E2%29
h=sqrt%2864-16%29
h=sqrt%2848%29cm

the area of the smaller of the two concentric circle is r=h%2F2
r=sqrt%2848%29%2F2

the area of the smaller circle is:
A=r%5E2%2Api
A=%28sqrt%2848%29%2F2%29%5E2%2Api
A=%2848%2F4%29%2Api
A=12%2Api%2Acm%5E2