A circle has a radius of 6 inches. What would be the area of an inscribed equilateral triangle?

Question

15038 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-06T14:20:12

Area = 27#sqrt(3)#

Length of a side of an equilateral triangle inscribed in a circle = #rsqrt(3)# , where r is the radius of the circle

Therefore, Area = #sqrt(3)a^2/4#
# a = 6sqrt(3)#

Note: how to get the above relation?
enter image source here

#a/sinA= c/sinC#

#=> c=a*(sinC/sinA) = 6*(sin 120/sin 30) = 6sqrt(3) #