Find the area of the shaded region. Express your answer in terms of pi.?

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  • David
    Lv 7
    4 weeks ago

    Shaded region: Area of rectangle - area of 3 circles = 335 square inches to nearest whole number

  • 4 weeks ago

    1st find the area of each circle..

    find the radius of each circle

    r = d/2

    r1 = 6/2 = 3

    r2 = 9/2 = 4.5

    r3 = 12/2 = 6

    Apply Area of a circle

    A = πr^2

    A1 = π(3)^2 = 9π

    A2 = π(4.5)^2 = 20.25π or 81/4π

    A2 = π(6)^2 = 36π

    Solving the area of a rectangle

    A = LW

    A = (3 + 6 + 9 + 12)(18)

    A = (30)(18)

    A = 540 square units

    Now solving the area of a shaded region.

    Area of shaded region = 540 - (9π + 81/4π + 36π) = 540 - 261/4 π or 335 square units answer//

  • 4 weeks ago

    The area of the shaded region:

     [540  - (9pi + 81/4 pi + 36 pi)] in^2

    = (540 - 65 1/4 pi) in^2 

    = 540 - 204.9894 in^2

    = 335 in^2

  • 4 weeks ago

    Looks like it's a rectangle minus 3 circles.

    The circles seem to have diameter 6, 9, and 12, so their radii are half of those: 3, 4.5, and 6. So there areas are pi*3^2, pi*4.5^2, and pi*6^2, which is 9*pi, 20.25*pi, and 36*pi, for a total of 65.25.

    The rectangle is shown as having a width of 18 and a height of 3 + 6 + 9 + 12 = 30, so its area is 30 * 18 = 540

    Final answer: 540 - 65.25*pi =~ 335.01107935326599119031251924101

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  • 4 weeks ago

    Let me first assume given is a rectangle. Area of a circle whose diameter is d, is (π/4)d^2.

    The shaded area = 18*(12+9+6+3) - (π/4)[12^2+9^2+6^2+3^2] = 540 - 135π/2.

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