split the square diagonally in half and count the fraction of each side, before adding them up.

For triangle ABD, by drawing the lines on the triangle you can divide it into 8 smaller triangles, 2 of which are shaded. Thus the ratio of the shaded area to the area of triangle ABD is 2 :8, when written in fraction would be 2/8 = 1/4 when simplified.

For triangle DBC, the smaller triangles have been drawn out correctly. The number of smaller triangles shaded is 8, where the total number of smaller triangles is 18. Hence the ratio of the shaded area in DBC to the area of DBC is 8:18, when written in fraction would be 8/18 = 4/9 when simplified.

Adding both fractions up, 4/9 + 1/4, the answer is 25/36, which thus gives the ratio =

total shaded area : area of the square ABCD
25 : 36
as the final answer.