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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?
  • a)
    128 square meters
  • b)
    154 square meters
  • c)
    162 square meters
  • d)
    172 square meters
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The figure below has been obtained by folding a rectangle. The total a...
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.
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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?a)128 square metersb)154 square metersc)162 square metersd)172 square metersCorrect answer is option 'C'. Can you explain this answer?
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