Sarin, Hairu and Fatimah make greeting cards for Mother’s Day part 19 (Math Question)

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

You can read the story of Sarin and the siblings making greeting cards for their mother by reading the posting on Sarin, Hairu and Fatimah make greeting cards for Mother’s Day in Welcome page.

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

You can read also the posting on Sarin learns concept of ratio in school to understand the concept of Ratio.

Read the posting on Sarin learns Symbol, Algebra and Equation in school (Math Concept) to understand the concept of Algebra

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

Upper primary school mathematics question UPQ531

Sarin using two pieces of identical right-angled triangle shape papers to make a special greeting card for his mother. He overlapping the two pieces of papers as the figure below, not drawn to scale, shown. Find the area of the blue region ABCD, where AD = 3 cm.

UPQ531-1

 

 

Solution:

UPQ531-2

Since the two pteces of triangular shape paper are identical and overlapped as shown,

The overlapped area is EDC.

So,

The area of EFGD is equal to the area of ABCD.

The area of ABCD = 5 × 6 + ½ × 3 × 5 = 37.5 cm2

Alternative solution:

Using ratio and Algebra expression,

UPQ531-3

By ratio,

CE : EF = FG : DA

If  CE = X cm

X/(X – 5) = 9/(9 – 3) = 3/2

2X = 3X – 15

X = 15 cm

The area of the triangle BEA = ½ × 15 × 9

The area of the triangle CED = ½ × 6 × 10

The area of the blue region ABCD = ½ × 15 × 9 – ½ × 6 × 10 = 37.5 cm2

  More Questions on Area. Click here…

More Questions on Ratio. Click here….

                                      

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