XAT 2015 Quant & DI Q4: Mensuration

This aptitude question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. A total of 33 questions appeared in this section in XAT 2015. This one is a medium level difficulty question and tests the concept of area of a rectanglular sheet. Question 4 of 33 questions that appeared in this section in XAT 2015.

Question

The figure below has been obtained by folding a rectangle. The total area of the figure (as visible) is 144 square meters. Had the rectangle not been folded, the current overlapping part would have been a square. What would have been the total area of the original unfolded rectangle?

1. 128 square meters
2. 154 square meters
3. 162 square meters
4. 172 square meters
5. None of the above

  Correct Answer      Choice C. The total area of the original unfolded rectangle is 162 square meters.

Explanatory Answer

Folded part as shown in the first figure is a triangle - a right triangle.


The two perpendicular sides of the right triangle measure 6m each. So, the triangle is a right isosceles triangle.

When unfolded the folded area becomes a square as shown in the following figure.

The side of the square will be the width of the larger rectangle and is therefore, 6m.

Area of the square = 6 * 6 = 36 sq.m

When folded, only the area of the right triangle gets counted.
However, when unfolded the area of square gets counted.
The square comprises two congruent right triangles.

In essence, when folded only half a square is counted. When unfolded the entire square gets counted.

The area of the rectangle when unfolded = area of the rectangle when folded + area of half a square.
So area after unfolding= 144 + 18 = 162 sq.m.

  The correct answer is Choice C.

Video Explanation