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Sector from its perimeter (2r + arc): find area or angle

This type of question, asked 2 times: 9 Sep 2024 S3, 10 Sep 2024 S3. All 2 questions below, oldest first.

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  1. Question 1

    9 Sep 2024 S3

    60
    Find the area (in cm2\text{cm}^2) of the sector whose perimeter is 643\frac{64}{3} cm and central angle is 60∘60^\circ. (Use π=227\pi = \frac{22}{7}.)

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  2. Question 2

    10 Sep 2024 S3

    67
    What is the central angle of a sector of a circle whose area and perimeter are, respectively, equal to 209 cm2\text{cm}^2 and 63 cm if it is given that its radius is a non-negative integer (roundup to one decimal place)?

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