Posted by buzz on Saturday, May 18, 2013 at 6:50pm.
find the area of a circle circumscribed about a equalateral triangle whose side is 18 inches long

geomerty  MathMate, Saturday, May 18, 2013 at 7:04pm
There are different ways to solve for the circumscribed radius, depending on which part of geometry you are working on.
The most basic calculation taking advantage that the triangle ABC is equilateral is to construct a perpendicular bisector on side BC such that ABD is a right triangle rightangled at D.
AD is then the median, and the radius of the circumscribed circle is 2/3 of AD.
Using Pythagoras Theorem,
AD=sqrt(AB^2BD^2)=sqrt(18^29^2)=sqrt(243)=9sqrt(3).
The radius of the circumscribed circle is therefore (2/3)*9sqrt(3)=6sqrt(3).
A more general method is
radius of circumscribed circle
=a/(2sin(A))
where a is any side of the triangle, and
A is the angle opposite side a.
Applied to the given equilateral triangle,
a=18
A=60°
so
r=18/(2sin(60)=6sqrt(3)
Answer This Question
Related Questions
 geometry  Find the area of a circle circumscribed about an equilateral triangle...
 Ms. Sue Please help!!!  Ahhh... thank you "A square and an equilateral triangle...
 Geometry  Problem : Howm do you find the area of a circle circumscribed about a...
 geometry  Open that link please please help me with my assignments 1. in the ...
 math  A circle is circumscribed about an equilateral triangle with side lengths...
 Geometry  Bob  Problem : Howm do you find the area of a circle circumscribed ...
 geomerty  two sides of a triangle have lengths 45 inches and 50 inches. How ...
 college algebra2  a triangle whose base is 18 inches long has an area of 280 ...
 mathematics  if a circle has a radius of 6 inches,what will the area of the ...
 GEOMETRY URGENT PLEASE  (imageshack)(.)us(/)photo (/) myimages (/)42(/)2vja. ...
More Related Questions