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primary 6 | Maths
| Measurement
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Date Posted: 1 month ago
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For every repeated pattern, the radius of semicircle on top is:
(34 - 10 - 10) ÷ 2 = 7 cm
Arc length of each semicircle is:
3.14 x (7 x 2) ÷ 2 = 21.98 cm
Below each semicircle, there are 2 quarter circles on the left and 2 more quarter circles on the right.
For each small quarter circle, the radius is 10 cm as given.
Arc length of each small quarter circle is:
3.14 x (10 x 2) ÷ 4 = 15.7 cm
For each big quarter circle, the radius is:
10 + 7 = 17 cm
Arc length of each big quarter circle is:
3.14 x (17 x 2) ÷ 4 = 26.69 cm
For each repeated pattern, the perimeter is:
21.98 + 2 x (15.7 + 26.69) = 106.76 cm
Next, we find the total number of repeated patterns:
153 ÷ 34 = 4.5
Since the perimeter of each repeated pattern is 106.76 cm,
106.76 x 4.5 = 480.42 cm
Last but not least, we need to include the 7-cm edge at the very beginning of the 1st pattern, as well as the 7-cm edge at the very end of the last 0.5 pattern:
480.42 + 7 + 7 = 494.42 cm
The answer is 494.42 cm.
(34 - 10 - 10) ÷ 2 = 7 cm
Arc length of each semicircle is:
3.14 x (7 x 2) ÷ 2 = 21.98 cm
Below each semicircle, there are 2 quarter circles on the left and 2 more quarter circles on the right.
For each small quarter circle, the radius is 10 cm as given.
Arc length of each small quarter circle is:
3.14 x (10 x 2) ÷ 4 = 15.7 cm
For each big quarter circle, the radius is:
10 + 7 = 17 cm
Arc length of each big quarter circle is:
3.14 x (17 x 2) ÷ 4 = 26.69 cm
For each repeated pattern, the perimeter is:
21.98 + 2 x (15.7 + 26.69) = 106.76 cm
Next, we find the total number of repeated patterns:
153 ÷ 34 = 4.5
Since the perimeter of each repeated pattern is 106.76 cm,
106.76 x 4.5 = 480.42 cm
Last but not least, we need to include the 7-cm edge at the very beginning of the 1st pattern, as well as the 7-cm edge at the very end of the last 0.5 pattern:
480.42 + 7 + 7 = 494.42 cm
The answer is 494.42 cm.
Thank u
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