You've got the first part right.


Now you should add the two fractions together.

6/54 + 9/54 = 15/54

so 15/54 of the area of the square = 10cm²

Area of the square = 10cm² x 54/15

= 36cm²

36cm² = 6cm x 6cm

So each side of the square is 6cm



OR


1/9 = 2/18
1/6 = 3/18

2/18 + 3/18 = 5/18

So 5/18 of the square's area = 10cm²

Square's area = 10cm x 18/5 = 36cm²

Combine Q and R together to get a bigger triangle.

Area of this triangle = ½ x 6cm x 6cm
= ½ x area of the square

So fraction of the square that is S

= 1 - fraction that is the bigger triangle - fraction that is P

= 1 - ½ - 1/9

= 7/18

@ "J". Your suggested answer should be the correct one. I have the same working like yours. (Same conceptual idea but the steps are slightly different)

Cool. Thanks for the affirmation