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Triangle formed by joining midpoints has one-fourth the area

This type of question, asked 3 times: 18 Jul 2023 S1, 11 Sep 2024 S2, 13 Sep 2024 S2. All 3 questions below, oldest first.

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  1. Question 1

    18 Jul 2023 S1

    71
    Let A, B, C be the mid-points of sides PQ, QR PR, respectively, of △PQR\triangle PQR. If the area of △PQR\triangle PQR is 32cm232\text{cm}^2, then find the area of △ABC\triangle ABC.

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  2. Question 2

    11 Sep 2024 S2

    55
    In △\triangle PQR, M, N, and S are the mid-points of sides PQ, PR and QR, respectively. If the area of the △\triangle PQR is 46 cm2\text{cm}^2, what is the area (in cm2\text{cm}^2) of the quadrilateral MNRQ?

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  3. Question 3

    13 Sep 2024 S2

    61
    ABC is an equilateral triangle. P, Q and R are the mid-points of sides AB, BC and CA, respectively. If the length of the side of the triangle ABC is 11 cm, then the area (in cm2\text{cm}^2) of Δ\DeltaPQR is:

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