Thread: Find the area of the shaded region

What is the area of the shaded region in this shape ؟
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Originally Posted by Mhmh96

What is the area of the shaded region in this shape ؟
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Are the shaded areas made from intersecting quarter circles?

Hello, Mhmh96!

You should have supplied more information.
Even if your diagram were symmetric, we're not sure what the figure is.

I'll assume that "Prove It" was correct . . . These are quarter-circles.

Code:

              * * *           * * *
          *           *   *           *
        *               *               *
       *               *:*               *
                       :::
      *               *:::*               *
      *               *:::*               *
      *               *:::*               *
             .*.*.*.   :::   .*.*.*.
       *  *:::::::::::**:**:::::::::::*  *
        *:::::::::::::::*:::::::::::::::*
       *  *:::::::::::**:**:::::::::::*  *
              * * *    :::    * * *
      *               *:::*               *
      *               *:::*               *
      *               *:::*               *
                       :::
       *               *:*               *
        *               *               *
          *           *   *           *
              * * *           * * *

Your diagram says the length of two "petals" is 4 units.
Then the radius of the circles is

I'll let you work out the details.

I get an answer of

Yes quarter-circles,but how did you find the radius ?

Hello, Mhmh96!

How did you find the radius?

Code:

              * * *
          *           *
        *               *
       *                 *
                          
      *         C         *
      *         o         *
      *    r  *   *  r    *
            *.*.*.*.*
       *  *:::::::::::*  *
      A o - - - - - - - o B
       *  *:::: 2 ::::*
              * * *           
      *                   *
      *                   *
      *                   *

       *                 *
        *               *
          *           *
              * * *

Chord is 2 units long.

Triangle is an isosceles right triangle.

Hence, its legs (the radius) is: