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primary 6 | Maths
| Geometry
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Date Posted: 2 years ago
Views: 488
Area of circle : Area of triangle
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
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
b)
Total shaded area
= 3B + 3C
= 2 parts + 5 parts
= 7 parts
= 7 × 16cm²
= 112cm²
Ratio of shaded to unshaded
= 112 : 40
= 14 : 5
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
done
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Hope it helps :)
Date Posted:
2 years ago
Word explanation in main comments section.
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
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
done
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Date Posted:
2 years ago
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