Ration of Areas

[jatinet]

A painter painted a white circular area, which is inscribed a blue square. When he finished, what is the ratio of the blue area to the whole square?

please explain your answers

[800ForSure]

Let's say the radius of the circle is r so the sides of the square will be 2r

Area of white = area of circle =A1= PIE*R^2
Area of Blue part =A2 = Area of Square-Area of Circle = 4R^2-A1

Ratio = R^2( 4-PIE)/4R^2 = [4-PIE]/4

[Dragonfinity]

Let r = radius of circle, then each side of the square will be 2r because it is inscribed. Hence,

Area of circle (white part) = pi*(r^2)
Area of square = (2r)^2 = 4*(r^2)
Area of Blue part = Area of square - Area of circle = 4*(r^2) - pi*(r^2) = (4 - pi)*(r^2)

Ratio of Blue part to whole square = [(4 - pi)*(r^2)]/[4*(r^2)] = (4 - pi)/4