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.