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Quadrilateral area from a diagonal and the perpendiculars to it from the other vertices

The same question, asked 2 times: 8 Aug 2022 Tier II*, 20 Jan 2025 Tier II. Every wording below, oldest first.

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  1. Question 1

    8 Aug 2022 Tier II

    32
    ABCD is a quadrilateral. The length of diagonal AC is 24 cm. The sum of perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral?

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  2. Question 2

    20 Jan 2025 Tier II

    18
    ABCD is a quadrilateral in which diagonal BD = 70 cm, AL⊥BDAL \perp BD and CM⊥BDCM \perp BD such that AL = 18 cm and CM = 20. Find the area (in cm2\text{cm}^2) of the quadrilateral ABCD.

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