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You shuold read the posting on Sarin learns Perimeter, Area and Volume in school(Math Concept) to learn the concept of Area.
Challenge yourself to solve the question before look out for the given solution‼
Upper primary school mathematics question UPQ259
After tidying up the house, Fatimah’s mother sews a piece of carpet to use during Hari Raya Puasa. The carpet has a brown outskirt with 10cm wide and fills with yellow and purple circles with identical size. A green cloth is used as the centre piece of the full carpet. The figure below showed a quarter of the carpet design. If there are 38 circles in total in a quarter of the carpet,
a) Find the outskirt area that is not covered by the circles.
b) Find the perimeter and area of the green cloth.
Base on a quarter of the carpet.
The length of a quarter of brown outskirt = 10 × 38 ÷ 2 ÷ 2 = 95cm
The area of a quarter of the brown outskirt = 95 × 10 = 950cm2
The radius of each circle = 10 ÷ 4 =2.5cm
The area of 38 circles = 38 × π × 2.5 × 2.5 = 38 × 3.14 × 2.5 × 2.5 = 745.75cm2
The area of a quarter of the outskirt not cover with circles = 950 – 745.75 = 204.25cm2
The area of the outskirt not cover with circles = 4 × 204.25 = 817cm2
Base on a quarter of the carpet,
Consider only the inner ring circles,
Set the number of inner ring circles as X and Y respectively
X + Y = (38 – 4) ÷ 2 = 17
The length of (X + Y) = 17 × 10 ÷ 2 = 85cm
The perimeter of the green cloth = 4 × 85 = 340cm
Assume maximum size for the carpet
17 ÷ 2 = 8R1
X = 8 and Y = 9
The length of X = 8 × 10 ÷ 2 = 40cm
The length of Y = 9 × 10 ÷ 2 = 45cm
The area of a quarter of the green cloth = 40 × 45 = 1800cm2
The area of the green cloth = 4 × 1800 = 7200cm2