Mathematics

Question

please respond asap!!!
please respond asap!!!

2 Answer

  • ANSWER

    [tex]9(\pi - \frac{ \sqrt{3} }{2} )[/tex]

    Approximately, A=20

    EXPLANATION

    The circle has radius r=3 units.

    The height of the triangle is ,

    [tex]h = 6 \cos(60 \degree) = 3[/tex]

    The base of the triangle is

    [tex]b = 6 \sin(60 \degree) = 3 \sqrt{3} [/tex]

    The area of the triangle is

    [tex] \frac{1}{2} bh[/tex]

    [tex] = \frac{1}{2} \times 3 \sqrt{3} \times 3[/tex]

    [tex] = \frac{9}{2} \sqrt{3} [/tex]

    The area of the circle is

    [tex]\pi {r}^{2} [/tex]

    [tex] = {3}^{2} \pi[/tex]

    [tex] = 9\pi[/tex]

    The difference between the area of the circle and the triangle is

    [tex]9\pi - \frac{9}{2} \sqrt{3} = 9(\pi - \frac{ \sqrt{3} }{2} )[/tex]

  • Answer:

    Difference = 20.47 square  units

    Step-by-step explanation:

    Points to remember

    Area of circle = πr²

    Where r - Radius of circle

    Area of triangle = bh/2

    Where b - Base and h- Height

    It is given a circle with radius 3 units

    And a right angled triangle with angles 30, 60 and 90 and hypotenuse = 6 units

    To find the area of circle

    Here r = 3 units

    Area =  πr²

     = 3.14 * 3 * 3

     = 28.26 square units

    To find the area of triangle

    Here sides are in the ratio Base : Height : hypotenuse = 1 : √3 : 2

     = Base :  Height : 6

     = 3 : 3√3 : 6

    Base b = 3 and height h  = 3√3

    Area = bh/2

     = (3 * 3√3)/2

     = 7.79 square units

    To find the difference

    Difference = 28.26 - 7.79

     = 20.47 square  units

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