The blog postings are about the Singapore Math. The readers can learn from the postings about 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 can learn the skills of dealing with Math Modeling, Problem Sum from Lower Primary School to Upper Primary School level after reading the postings. This posting is an upper primary school math question on Area and Problem Solving.

You can read the posting on **Sarin’s family and Ramadan** and **Sarin’s family celebrating Hari Raya Puasa** in Welcome page about story of Sarin’s family during Ramadan and celebrating Hari Raya Puasa.

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 UPQ258**

Sarin is cleaning up a storage shelf during Ramadan. He has 7 identical blue boxes to place on the shelf. If he arranges the blue boxes on the shelf as in figure 1, he find out that he can only place 6 blue boxes on it. When he rearranges the blue boxes as figure 2 shown, he manages to place all the blue boxes on the shelf. Figures are not to scale.

a) Find the length of the gap G.

b) Find the height of the shelf.

c) How Sarin should position the 7^{th} box in the shelf in Figure 2?

Solution:

The boxes are identical so the area, breadth and length of the boxes are measured the same or same in size.

Approach the question by considering only 6 boxes on the shelf as figure 1 arrangement only can take in 6 boxes.

The 6 boxes occupied same area in both figures. As well as the unoccupied area are the same in both figures.

1m = 100cm

The area of the unoccupied space = 60 × 0.9 × 100 = 5400 cm^{2}

The breadth of the box = 0.9 × 100 ÷ 2 = 45cm

In figure 1, the area of the unoccupied space is in the shape of two rectangles

The area of rectangle B = 4 × 45 × G = 5400 – 10 × 0.9 × 100 = 4500 cm^{2}

The gap G = 4500 ÷ 4 ÷ 45 = 25cm

The length of the box = 90 – 25 = 65cm

The height of the cupboard = 60 + 3 × 65 = 255cm

Sarin only can place the 7^{th} box in horizontal position in the shelf in figure 2.