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Annie Lim
Annie Lim

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Please help, thanks

Date Posted: 1 week ago
Views: 11
1 week ago
Draw 3 lines, 1 each from A, B and C to the centre of the central circle.

You'll notice the equilateral triangle is divided equally into 3 parts.
Annie Lim
Annie Lim
1 week ago
How to do the working? Please advise, thanks.
1 week ago
Radius of circle = 7cm

Area of circle = 22/7 x 7cm x 7cm = 154cm²

Area of 3 outer shaded segments
= area of circle - area of equilateral triangle
= 154cm² - 56cm²
= 98cm²

How to find the shaded area inside the equilateral triangle :

Method ①

Area of 1 segment = 98cm² ÷ 3
= 32⅔cm²

Dividing the equilateral triangle into 3 equal parts,

Area of each smaller triangle
= 56cm² ÷ 3 = 18⅔cm²

The inner segments and outer segments are equal. Subtract the area of smaller triangle from area of segment,

32⅔cm² - 18⅔cm²
= 14cm²

14cm² = 2 small half-leaves
There are 6 small half-leaves inside the equilateral triangle.

Area of 6 leaves = 14cm² x 3 = 42cm²

So total area of shaded parts
= 98cm² + 42cm²
= 140cm²

Method ②

Notice the 3 segments in the inside of the equilateral triangle overlap. They are equal in area and they are identical to the other segments.

Adding them together will result in double counting of each small leaf. 3 small leaves are over counted.

The 3 inner segments also include the unshaded area inside the equilateral triangle.

3 inner segments 3 outer segments
= 98cm² (outer segment is obtained as shown in the first step)

When we subtract the area of the equilateral triangle from this 98cm², we remove the unshaded area, and also remove those 3 double counted small leaves.

98cm² - 56cm² = 42cm²

The remaining area is that of 3 small leaves, which is 42cm².

Total area of shaded parts = 42cm² + 98cm² = 140cm²

So we don't have to actually divide the by 3 to find the value of two half-leaves first and then find 6 half-leaves.
Annie Lim
Annie Lim
1 week ago
Thank you!
1 week ago