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Area = (1/2) ab sin C for a triangle, or ab sin C for a parallelogram

This type of question, asked 4 times: CDS 1 2022, CDS 2 2024, CDS 1 2025, CDS 2 2025. All 4 questions below, oldest first.

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  1. Question 1

    CDS 1 2022

    74
    ABCDABCD is a parallelogram with AB=15AB = 15 cm and AD=8AD = 8 cm. If θ\theta is the acute angle between ABAB and ADAD, then what is the area of the parallelogram in square cm?

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  2. Question 2

    CDS 2 2024

    19
    In a triangle ABCABC, ∠ABC=60∘\angle ABC = 60^\circ and ADAD is the altitude. If AB=6AB = 6 cm and BC=8BC = 8 cm, then what is the area of the triangle ?

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  3. Question 3

    CDS 1 2025

    17
    The adjacent sides of a parallelogram are 10 cm and 8 cm and the angle between them is 150∘150^\circ. What is the area of the parallelogram ?

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  4. Question 4

    CDS 2 2025

    71
    In a triangle ABCABC, ∠A=30∘\angle A = 30^\circ, AB=7AB = 7 cm and AC=12AC = 12 cm. What is the area of the triangle ABCABC?

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