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primary 5 | Maths
| Area & Volume

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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

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

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