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Folded Rectangle Area

XAT 2015 · Quantitative Ability & Data Interpretation · Medium · Geometry

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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?

[Height of square fold =6m, width segment =14m]\text{[Height of square fold } = 6\text{m, width segment } = 14\text{m]}

  1. A.

    128 square meters

  2. B.

    154 square meters

  3. C.

    162 square meters

  4. D.

    172 square meters

Answer

C

Explanation

When the rectangle is unfolded, the overlapping triangular part △BCE\triangle BCE is added back to the visible area.

Since BC=CE=6 mBC = CE = 6\text{ m}, area of △BCE=12×6×6=18 sq. m\triangle BCE = \frac{1}{2} \times 6 \times 6 = 18\text{ sq. m}.

Total area of original unfolded rectangle =144+18=162 sq. m= 144 + 18 = 162\text{ sq. m}.

Hence, option C is correct.

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