Which figure has a greater area? To the nearest tenth, how much greater is the area?

Question

A math teacher draws an equilateral triangle with radius 6 inches and a square with the same radius. 

Answer 1

usually "radius" refers to a property of circles, not triangles or squares

the more sides a polygon has, the more area is has for a given perimeter

for a circle the "perimeter" is the circumference. the circle has greatest areas for given "perimeter"

a circle is like a polygon with infinite number of sides.

Triangle has the least number of sides and for any comparable property to a radius, it would have

less area than a square.

maybe by 'radius" you mean the distance from the center to some point on the polygon. For

a triangle that might be the distance from the center to the nearest base or sqr3/2 for a triangle with sides = 2 each.

for a square that might mean the distance from the center to any side or sqr3/2 if each side = sqr3

area for that square is 3, area for the triangle is (1/2)sqr3 = sqr3/2. the square has greater area.