Sarin learns Perimeter, Area and Volume in school part 92 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids can acquire the skill of dealing with the Math Modeling, the Math Problem Solving and the Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Fraction,  Area and shape.

You can read posting Sarin learns Perimeter, Area and Volume in school(Math Concept) to learn the concept of perimeter and area.

Read also the posting on Sarin learns Shapes and Solids in school (Math Concept) to know about shapes.

Read the posting on Sarin learns the concept of Fraction (mathematics concept) to understand the concept of Fraction.

Challenge yourself with the question before look out for the given solution‼!

Upper primary school mathematics question UPQ415

The diagram is not drawn to scale. ABCD is a square and arc BD is a quarter with centre point at C. What is the fraction of the area of the yellow region in the figure ABCD? If AB = 20 cm, calculate the area of the yellow region (Take π = 3.14)

UPQ415-1

Solution:

 UPQ415-2

            Figure ABCD is a square

            AB = DC = 20 cm

            AC bisect the square to two identical isocelete triangles

            ∠ DAG = ∠ FEC = ∠ FCE = 450

            AD = DC and EF = FC

            Similarly,

            DG = GC and ∠ GDC = ∠ ECF

            Arc BD is a quarter with centre point at C

            EC = DC = AB

            Triangle DGC is identical to triangle EFC

            Fit triangle EFC to the position of triangle DGC as below diagram shown

UPQ415-3

            The fraction of the yellow region is ¼ of the figure ABCD.

            The area of the figure ABCD = 20 × 20 = 400 cm2

            The area of the yellow region = 400 ÷ 4 = 100 cm2

            Please note that the solution also shown that the area of a square X is half the area of a square Y, if the diagonal length of square X is equal to the side length of square Y.

 More Questions on Area. Click here….

More Questions on Fraction. Click here….

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