Area

$We \space know \space , \space if \space a \space \triangle \space and \space a \space Parallelogram \space lie \space on \space the \space same \space \space base \space and \space between \space same \space parallels$

$then \space Area \space of \space \triangle \space=\space \frac{1}{2} \space \times \space Area \space of \space Parallelogram$

$\Rightarrow Area \space of \space green \space region \space=\frac{1}{2} \space \times \space \space Area \space of \space Rectangle$

$\Rightarrow Area \space of \space blue \space region \space+\space Area \space of \space green\space region\space=\space Area\space of \space Rectangle$

$\therefore \space Area \space of \space blue \space region \space= \space Area \space of \space green\space region \space=\space \boxed{25}$

Split the green triangle into 2 right triangles.You will see that the triangles will be equivalent in size to the other corresponding blues so the blues and the greens must be equal.

The area of the green triangle = (1/2)bh = 25. Let the top side of the rectangle be split into x and b - x, each being met by the green triangle vertex Then the blue area = (1/2)bx + (1/2)x(b - x) = (1/2)bh = 25. Ed Gray

Let the base the triangle be $b$ and its height be $h$ . Then, we have:

$Area\space of\space the\space triangle\space =$ $\frac{1}{2}\space \times\space b\space \times\space h\space =\space 25$

$\Rightarrow\space b\space \times\space h\space =\space 50$ . So, the area of the rectangle is 50.

$\therefore\space Area\space of\space the\space blue\space region\space =\space Area\space of\space the\space rectangle\space -\space Area\space of\space the\space green\space region\space =\space 50\space -\space 25\space =\space 25$ .