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Area of Inscribed Triangle in Square

XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Geometry

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In a square PQRS, A and B are two points on PS and SR such that PA = 2AS, and RB = 2BS If PQ = 6, the area of the triangle ABQ is (in sq. cm)

  1. A.

    6

  2. B.

    8

  3. C.

    10

  4. D.

    12

  5. E.

    14

Answer

C

Explanation

Square side = 6. Area(PQRS) = 36. PA=4,AS=2PA = 4, AS = 2, RB=4,BS=2RB = 4, BS = 2. Area(△APQ\triangle APQ) = 12×6×4=12\frac{1}{2} \times 6 \times 4 = 12. Area(△RBQ\triangle RBQ) = 12×6×4=12\frac{1}{2} \times 6 \times 4 = 12. Area(△ASB\triangle ASB) = 12×2×2=2\frac{1}{2} \times 2 \times 2 = 2. Area(△ABQ\triangle ABQ) = 36−(12+12+2)=1036 - (12 + 12 + 2) = 10 sq. cm.

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