Find the area of the shaded region, circle and parallelogram

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The area of the parellelagramm is base times height. You know figured out the height. So the base is the radius of the circle. You know that.

What is the area of the circle wedge? Well the entire circle is 360 degrees so this is just 30 degrees. It's a specific proportion of the entire circle. So if you can find the area of the entire circle you can find the area of the circle wedge.

The area of the shaded area is the area of the paralelagram minus the area of the circle wedge.

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Dana
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Dana

Updated on December 23, 2020

Comments

  • Dana
    Dana almost 3 years

    Given a circle with center A and radius 2. If ABCD is a parallelogram, find the area of the shaded region. Image that can with the problem

    I am having trouble with this problem. I know that:

    -This is a 30:60:90 triangle, so the height is 1, and the other side length is root 3. Also, segment CD is also 2, and angle BCD is 30° because it is a parallelogram

    ...and that's pretty much it. Could someone help explain how to solve the rest of the problem?

    • fleablood
      fleablood about 8 years
      Find the area of the parellelagram, the area of the circle arc. And subtract.
    • Joel Cohen
      Joel Cohen about 8 years
      Can you compute the area of the parallelogram ? Then try to compute the area of the section of disc $ABD$.
  • Dana
    Dana about 8 years
    How would one find the area of the circle wedge?
  • fleablood
    fleablood about 8 years
    30 degrees is 1/12 of 360 degrees so the area of the wedge will be 1/12 of the area of the circle.
  • Dana
    Dana about 8 years
    Okay. I think I'm understanding it now. So I find the area of the circle, take 1/12 of that, and subtract that value from the area of the parallelogram?