Question says both shaded triangles are of equal area. So we make the numerator the same for both fractions since the number of units shaded is the same.

2/7 of square is shaded.
This is the same as saying 2 units out of 7 units are shaded.

We change 1/9 of rectangle to = 2/18 of rectangle. Now the numerators are the same.

This is the same as saying 2 units out of 18 units are shaded.

So we can say :
① Each shaded triangle's area is 2 units
② Area of square is 7 units
③ Area of rectangle is 18 units.


Total area of square and rectangle
= 7 units + 18 units
= 25 units

25 units = 175cm²
1 unit = 175cm² ÷ 25 = 7cm²

Total area of the two shaded triangles
= 2 units + 2 units
= 4 units
= 4 x 7cm²
= 28cm²

Since ¼ of the triangle is shaded,
1 - ¼ = ¾
¾ of the triangle is unshaded.

¾ is just 3 times of ¼.

So unshaded area of triangle
= 3 x 28cm²
= 84cm²

Alternatively, continuing from your working,

1/9 rectangle = 2/7 □ = 1/8 △
2/18 rectangle = 2/7 □ = 2/16 △

Ratio of area of rectangle : □ : △
= 18 : 7 : 16

Total for rectangle and □ = 25 units

Working is same as above. But you can also find the unshaded triangle area by writing the following :

16 - 2 - 2 = 12
12 x 7cm² = 84cm²

Thank you so much.

You're most welcome!