SOLUTION: I need to find the exact area of a shaded region of a circle. The picture looks like there's a triangle in the middle of it and the sides of this triangle are 24m long... I just re

Algebra ->  Surface-area -> SOLUTION: I need to find the exact area of a shaded region of a circle. The picture looks like there's a triangle in the middle of it and the sides of this triangle are 24m long... I just re      Log On


   

Question 1010583: I need to find the exact area of a shaded region of a circle. The picture looks like there's a triangle in the middle of it and the sides of this triangle are 24m long... I just really need the way to find the shaded area of a circle... Thank you in advance!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe you hope to describe an equilateral triangle inscribed in a circle, and the side of the triangle is 24 meters.

Distance from center to any vertex where the circle and triangle meet is a radius. To be more brief in the discussion of the description, The equilateral triangle so inscribed is made of SIX special 30-60-90 triangles. Each has a leg 24%2F2=12, a hypotenuse r, and another leg r%2F2.

Find the radius.
%28r%2F2%29%5E2%2B12%5E2=r%5E2
Cutting past the algebra, highlight%28r=8sqrt%283%29%29.

You did not indicate what is and what is not shaded to find its area quantity. The area of the TRIANGLE will be 6%281%2F2%29%28base%29%28height%29, refering to the individual special right triangles...
The whole equilateral triangle area is 6%28%281%2F2%29%2812%29%281%2F2%298sqrt%283%29%29, the expression just enough for you to understand, ... and you can compute to finish.