Area Of A Fractional Pink Shade

A look at the question first!

Let's first recall the formula for the calculation of area of a triangle.

Area of triangle =  1/2 x Base x Height

Let's assume the side of the square is 1.

Now the triangle with the pink shade & triangle opposite to it are similar triangles. Similar triangles are triangle whose sides are in proportion with each other.

Since here base of pink triangle is double of un shaded opposite triangle, the height of pink triangle must be double of that smaller triangle.

But together, heights of both triangles must be equal to side of the square i.e. 1.

And hence, height of smaller triangle must be 1/3 & that of pink 2/3. (h + 2h = 3 ; h = 1/3).

So,

Area of Pink Triangle = 1/2 x Base x Height = 1/2 x 1 x 2/3 = 1/3.

So the area of pink shaded part is 1/3rd of total area occupied by square.