📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!


    ⚡ Azaadi sale - Celebrate Independence Day with Flat 55% Off On all courses! 13 to 17 Aug ⚡ Enroll Now

    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.

    Practice Next

    Relevant for Exams:

    ask-question

    Not sure which exam is best for you Talk to our expert

    Get My Free Call