Polygon

4meonly wrote:OA D

assuming right polygon = regular polygon


Clearly each statement is not sufficient

combined


diagnol of polygon = diameter of circle possible for polygon with sides 4,6,8... so on.



Area of polygon with 4 sides = 4* 1/2*r*r = 2r^2

area of cirecl = 22/7 * r^2

ratio = 2r^2 / (22/7 * r^2)= 7/11 = 0.636 < 2/3= 0.66

ratio of was to 2/3 but less than that.

definitely area of polygon with sides 6 > 0.66


C

sides=4

Ok Im getting C

St 1: You can have square or hexagon...INSUFF

St 2: doesn't give much information...INSUFF

Combining:

Square

Diameter of circle = diagonal of square = 2r
Side of square = r*sqrt2
Area of square = 2*r^2
Area of circle = Pi*r^2

Ratio of square to circle = 2/3.14<2/3

Hexagon: is a combination of 6 equilateral triangles

Side of hexagon = radius of circle = r
Area of hexagon = 6*[(sqrt3)/4]*r^2 = 3*[sqrt3/2]*r^2
Area of circle - Pi*r^2

Ratio of hexagon to circle = 3*1.7/3.1*2 = 5/6 (approx)>2/3

So the polygon has 4 sides.
Option C looks SUFF

Note: The polygon could be a rectangle or a square. I took square because square is the largest quadrilateral in a circle.

Are you sure of the OA 4meonly?

C for me as well!

1) gives many options: 4,6,8..... insuff

2)We r given Area of polygon/area of circle <2/3
Area of circle with radius x =&#8719;x²
Area of Triangle/area of cirlcle = (x²&#8730;3/2)/&#8719;x²= (approx)3/11<2/3
Area of square/area of cirlcle = (2x²/&#8719;x²) = 7/11<2/3
Area of square/area of hexagon=3&#8730;3x²/&#8719;x²=35.7/44>2/3
......insuff

combining 1 & 2 we get it is a 4 sided polygon