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## Question

primary 5 | Maths | Rate & Ratio

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##### Oliver

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how to do, tks

Date Posted: 1 month ago
Views: 20
J
1 month ago
The two smaller semicircles have radius 4.5cm. They can be combined to form 1 circle. Same for the two larger semicircles, which have a radius of 6cm.

Combined area of the two smaller semicircles
= 3.14 x 4.5cm x 4.5cm
= 63.585cm²

Combined area of the two larger semicircles
= 3.14 x 6cm x 6cm
= 113.04cm²

Area of rectangle
= 9cm x 12cm
= 108cm²

Notice the large unshaded circle in the middle. See the 15cm line? That's its diameter. So its radius is 7.5cm.

Area of large unshaded circle
= 3.14 x 7.5cm x 7.5cm
= 176.625cm²

= Area of all 4 semicircles + area of rectangle - area of large unshaded circle

= 63.585cm² + 113.04cm² + 108cm² - 176.625cm²

= 108cm²
Oliver
1 month ago
great tks

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##### Univia M.'s answer
1st
I hope this is correct cuz i’m P6:)
Date Posted: 1 month ago
J
1 month ago
Final answer is incorrect. Your approach to solving is correct but you've mistaken the diameter of the big unshaded circle to be 12cm instead of 15cm.

Also, there is a calculation error in your second last step. It should be 176.625cm² instead of 149.625cm².

Notice that the 15cm line cuts across the centre of the large unshaded circle. So the diameter is 15cm and therefore radius is 7.5cm

Tip :

Two semicircles of the same size can be combined into a single circle. So in your working, you can just write

½ x 3.14 x 6 x 6 x 2

Or

3.14 x 6 x 6

in a single step instead of dividing by ½ to find one semicircle and then multiplying by 2 again
Oliver
1 month ago
thats right, thanks