25. The diagram shows a quadrilateral divided into four smaller quadrilaterals with a common vertex $K$. The other labelled points divide the sides of the large quadrilateral into three equal parts. The numbers indicate the areas of the corresponding small quadrilaterals. What is the area of the shaded quadrilateral?
A 4
B 5
C 6
D 6.5
E 7
Solution
C

Label the four vertices of the quadrilateral $G, H, I$ and $J$ and join all four vertices to point $K$, as shown. Let the areas of triangles $G K P, S K I, I K T$ and $W K G$ be $x, y, z$ and $w$. Since triangles $P K H, H K S, J K T$ and $J K W$ have the same heights as triangles $G K P, S K I, I K T$ and $W K G$ but twice the base, their areas are $2 x, 2 y, 2 z$ and $2 w$, as shown. Therefore, since the sum of the areas of quadrilaterals $W K T J$ and $P K S H$ is $18+10=28$, we have $2 x+2 y+2 z+2 w=28$ and hence $x+y+z+w=14$. Hence $8+$ area $S K T I=14$ and therefore the area of the shaded quadrilateral in the question is 6 .