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    Question

    In parallelogram ABCD, point E is located on side AB,

    and line segment DE is drawn perpendicular to AB. Given that AD measures 5 cm, AB is 12 cm, and AE is 3 cm, determine the area of the parallelogram.
    A 44 cm² Correct Answer Incorrect Answer
    B 52 cm² Correct Answer Incorrect Answer
    C 60 cm² Correct Answer Incorrect Answer
    D 48 cm² Correct Answer Incorrect Answer

    Solution

    Image Since DE is perpendicular to AB, AED forms a right angled triangle whose hypotenuse is AD. Using Pythagoras theorem in triangle AED, So, ED2 = AD2 – AE2 = 52 – 32 = 25 – 9 = 16 So, ED = √16 = 4 cm Area of a parallelogram = base × height = AB × ED = 12 × 4 = 48 cm2

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