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    Question

    In ∆ PQR, M, N, and S are the mid-points of sides PQ,

    PR and QR, respectively. If the area of the ∆ PQR is 46 cm² , what is the area (in cm²) of the quadrilateral MNRQ?
    A 39 Correct Answer Incorrect Answer
    B 27.6 Correct Answer Incorrect Answer
    C 23 Correct Answer Incorrect Answer
    D 34.5 Correct Answer Incorrect Answer

    Solution

    Given: M, N, and S are midpoints of sides PQ, PR, and QR of triangle PQR. Area of ∆PQR = 46 cm².

    Join midpoints M, N, and S. Quadrilateral MNRQ is formed by removing triangle MNS from triangle PQR.

    Since MNS is formed by joining midpoints, it is similar to ∆PQR and has one-fourth its area.

    Area of ∆MNS = (1/4) × 46 = 11.5 cm²
    Area of quadrilateral MNRQ = 46 - 11.5 = 34.5 cm².

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