Area Problem #27

What fraction is shaded?



5 thoughts on “Area Problem #27

  1. I think it is 1/12 (One over twelve)
    Area of the shaded area ÷ Area of the square
    Area of the square = 5units×5units =25 units
    Area of the shaded area = (25units÷2)-(25units÷4)-(5units^2×2)^0.5÷6×(5units^2×2)^0.5) = 2.08333
    2.08333÷25 = 0.08333 = 1/12
    Am I right?

  2. La parte colorata è un deltoide che ha le diagonali lunghe l/2 ed l/3 ( con l lato del quadrato grande). La sua area è quindi l/2 x l/3 : 2 = l x l / 12. Quindi la dodicesima parte dell’area del quadrato che è l x l. CVD

  3. 1/12 – The triangle in the top right of the shaded area is bounded by a line with slope 1/2. It intersects with the line from the center with slope 1/1. The vertical sides of the two triangles add to 1/2. The top triangle vertical line is twice the bottom and so the sides are 2/6 and 1/6 because of the slope of the lines. The horizontal line, shared by both triangles composing the right half of the shaded area, is equal to the lower vertical line of length 1/6 because of the slope of that line of 1. Twice the area of these two triangles equals the entire shaded area since the right and left side of the shaded area are symmetric. This area = 2*[(1/2)*(2/6)*(1/6)+(1/2)*(1/6)*(1/6)] = (2/36) + (1/36) = 3/36 = 1/12. Dividing by the area of the unit square gives the ratio (1/12)/1 = 1/12.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s