Question
What is the perimeter of a regular hexagon with an area of 294ã3 ?
Answers
Reiny
I will assume your symbol is supposed to say 294√3
There are 6 identical triangles in a regular hexagon, so each triangle has an area of 49√3
Let the side of each triangle be x
all angles in each triangle are 60°
so (1/2)(x)(x)sin60° = 49√3
(1/2)x^2 (√3/2) = 49√3
x^2 = 196
x = 14
so the perimeter is 14(6) = 84
There are 6 identical triangles in a regular hexagon, so each triangle has an area of 49√3
Let the side of each triangle be x
all angles in each triangle are 60°
so (1/2)(x)(x)sin60° = 49√3
(1/2)x^2 (√3/2) = 49√3
x^2 = 196
x = 14
so the perimeter is 14(6) = 84