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primary 6 | Maths
| Geometry

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5 : 3

Their difference is :

5 units - 3 units = 2 units

Area of circle = areas A + C + C + C

= A + 3C

= 5 units

= 120cm²

So 1 unit = 120cm² ÷ 5 = 24cm²

Area of triangle = areas A + B + B + B

= A + 3B

= 3 units

So Difference = 2 units = 24cm² × 2 = 48cm²

But, difference also

= (A + 3C) - (A + 3B)

= A + 3C - A - 3B

= 3C - 3B

So 3C - 3B = 48cm²

And the ratio of 3C : 3B

= 5 : 2

So their difference is 5 - 2 = 3 parts

The difference is unchanged. Their common area is A so difference between whole circle and triangle = difference between 3C and 3B

So 3 parts = 2 units = 48cm²

1 part = 120cm² ÷ 3 = 16cm²

Area of unshaded part

= Circle area - 3C

= Circle area - 5 parts

= 120cm² - 5 × 16cm²

= 120cm² - 80cm²

= 40cm²

Or

Area of unshaded part

= Triangle area - 3B

= 3 units - 2 parts

= 3 × 24cm² - 2 × 16cm²

= 72cm² - 32cm²

= 40cm²

Total shaded area

= 3B + 3C

= 2 parts + 5 parts

= 7 parts

= 7 × 16cm²

= 112cm²

Ratio of shaded to unshaded

= 112 : 40

= 14 : 5

### See 3 Answers

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Model representation and ratio :

● →|A|C|C|C|

▲→|A|B|B|B|

● : ▲: (their difference)

5 : 3 : 2

shaded of ● →|C|C|C|

shaded of ▲→|B|B|B|

(shaded of ●) : (shaded of ▲) : (their difference)

5 : 2 : 3

The difference is unchanged/constant. So make the units the same.

Common multiple of 2 and 3 is 6 (2 x 3 = 6, 3 x 2 = 6)

● : ▲: (their difference)

5 : 3 : 2

15 : 9 : 6

(shaded of ●) : (shaded of ▲) : (their difference)

5 : 2 : 3

10 : 4 : 6

So now we have all the units the same size.

Circle area = 15 units = 120cm²

1 unit = 120cm² ÷ 15 = 8cm²

Unshaded area = 15 units - 10 units

= 5 units = 5 × 8cm² = 40cm²

Or

Unshaded area = 9 units - 4 units

= 5 units = 5 × 8cm² = 40cm²

b)

Shaded area = 10 units + 4 units = 14 units

Ratio of shaded to unshaded = 14 : 5

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