Question

Please help me with areas of regular polygons ♥

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

3-inch radius

Answer 1

I'm assuming they're talking about the circumradius

Answer 2

we have this equilateral triangle

Answer 3

from the center of the triangle to the vertex is the circumradius and we know it's 3 inches

Answer 4

drop a perpendicular line segment to one of the side to get this

Answer 5

Doesn't that make a 30, 60, 90 triangle??

Answer 6

now the circumradius cuts the angle of a the equilateral triangle in half

so we go from 60 degrees to 30 degrees

and yes, that forms a 30, 60, 90

Answer 7

the shorter leg is half of the hypotenuse, so the shorter leg is 3/2

the longer leg is sqrt(3) times longer than the shorter leg, making the longer leg to be (3/2)*sqrt(3) units long