CHIJ Katong 2007 Math Prelim
Question:
In the figure below, ABC is a right-angled triangle. AB = 12 cm and
BC = 16 cm. Find the area of the shaded parts.
(Leave your answer in terms of π)

From the above question, everyone can easily tell that it is a Circle question.

I used to tell my students that circle questions for primary 6 level are actually ‘free gift’ questions as all students should be able to score for this type of question if they knew the two formulas well; the circumference of a circle = π x d and the area of a circle = π x r x r

Based on my analysis of all Circle questions that appeared in the 2007 math prelim exam papers, I have to retract my above sentence as these questions are no longer ‘free gift’ questions.

Please study the above question and see if you can solve it?

I bet for some parents, even after I have provided you with my answer, you might still not be able to understand how it was done!

Once you are done with you solution, check yours with mine.

To find the shaded area, all you need to do is this:

Can you understand my solution or are you now confused !!!!!?????

Well, for this question, the challenge faced by most primary 6 students is that they are not able to find the area of the shaded parts individually!

To solve this question, not only your foundation of Circles topic needs to be strong, you must be stronger in your Visual Processing Cognitive Skills (your ability to see, rotate and hold the diagram in your mind as a whole or in parts)!

Well, let me explain my solutions.
To help you to see better, first, I will split the diagram into parts and label these parts as shown below:

If I split the given diagram into 2 semi circles and add them up, do you agree with me that the total (in terms of parts) is equal to A, B, C, C, D, D, X & Y. In short, I will have one part A, one part B, two part C, two part D, one part X and one part Y.

Now, let us look at what parts this triangle contains:

(this triangle has one part C, one part D, one part X & one part Y)

Therefore, when I use the sum area of 2 semi circles to subtract the area of a triangle, I will end up with parts A, B, C & D and these four parts actually make up shaded parts of the diagram. cool right? ...hehe

To illustrate using A, B, C, D …., this is how it is done:

I hope I have added an additional tool for your child to tackle “tougher” questions on Circles.

I will continue to post more challenging questions till the final day before the PSLE. So, please remember to check out this site frequently.

Cheers
Norman Tien

http://www.pslemath.com/

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