MBApyq

Area of Quadrilateral PQNM in Rectangle

XAT 2014 · Quantitative Ability & Data Interpretation · Hard · Geometry

All XAT 2014 questionsMore Geometry questionsAll XAT QADI

Consider a rectangle ABCD of area 90 units. The points P and Q trisect AB, and R bisects CD. The diagonal AC intersects the line segments PR and QR at M and N respectively. What is the area of the quadrilateral PQNM?

  1. A.

    9.5 and ≤ 10

  2. B.

    10 and ≤ 10.5

  3. C.

    10.5 and ≤ 11

  4. D.

    11 and ≤ 11.5

  5. E.

    11.5

Answer

D

Explanation

Area of △RPQ=16Area(ABCD)=15\triangle RPQ = \frac{1}{6} \text{Area}(ABCD) = 15. Using similar triangles, MR=35RPMR = \frac{3}{5} RP and NR=37RQNR = \frac{3}{7} RQ. Area(△RMN)=35×37×15=277≈3.86(\triangle RMN) = \frac{3}{5} \times \frac{3}{7} \times 15 = \frac{27}{7} \approx 3.86. Area(PQNM)=15−3.86=11.14(PQNM) = 15 - 3.86 = 11.14 sq units.

Related Geometry questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace