Challenging Question - Think Out of the Box

Question :

The figure below, not drawn to scale, is made up of 3 squares.  Find the area of the shaded parts

Ans :

Area of Big Rectangle = 18cm x 14cm
                                      252 cm²

Area of unshaded Big triangle = ¹/₂ * 14cm * 16cm
                                             = 112 cm²

Area of unshaded small triangle = ¹/₂ * 8cm * 8cm
                                                = 32 cm²

Area of Small unshaded Rectangle = 2cm x 6cm
                                                     = 12 cm²

Area of shaded parts = 252cm² - 112cm² - 32cm² - 12cm²
                                 = 96 cm²



                                                                                          Ans : 96 cm²

Explanation :

This question require a little thinking.  As the slope of the shaded parts extended from one square to the other, it do not cut perfectly at the corner of the 10cm square.  Therefore you will need to extend the boundary into a bigger rectangle and minus off the unshaded portion.  This type of question will train the students to think unconventionally. The diagram is illustrated separately at the bottom.

More Word Problem - 2 scenerios

Question :

Mr Tan bought a bag of sweets for his class.  If he gives 13 sweets to each of his pupils equally, he has 4 sweets left.  If he gives 8 sweets to each of his pupils equally, he has 214 sweets left. How many pupils are there in his class?

Method 1 :

Differences in sweets to each pupils        13 - 8 = 5
Difference in total of sweets left              214 - 4 = 210

Nos. of pupils  =  Difference in total of sweets left / Differences in sweets to each pupils
                      =  210 / 5 = 42


                                                                                    Ans : 42 pupils


Methods 2 :

Let the Nos. of pupils in the class be 1 unit
Total sweets = sweet gave + sweets left
        13 units + 4  =  8 units + 214
        13 units - 8 unit 214 - 4
                       5 units210
                       1 unit 210 / 5 = 42


                                                                                    Ans : 42 pupils

Remarks :

Many students approach to solve this type of problem with guess & check method.  Although it is one of the approve ways of solving the problem, personally, I feel it take more time with guess & check method.  With the above 2 methods, it will give student more time to check their test papers by solving the problem faster.  It is also my advice to student that whenever problem need to be solve by guess and check.  They should reserve it to the last and spend their time firstly on question that they can solve quickly.