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    Another way to do "Let's practice"?

    Module 2 Day 3 Challenge Part 4
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    • RZ923R
      RZ923 M0★ M2★ M3★ M4★ M5
      last edited by debbie

      Module 2 Week 1 Day 3 Challenge Part 4 Mini-Question

      I found another way to do the "Let 's practice" question.
      We can see by symmetry that the almond is a part of the square with side lengths \(1\). It can be made public two overlapping quarter circles with radius \(1\). The overlapping quarter circles each have an area of \( \pi / 4\), making the total \( \pi / 2\). The square, of course, have an area of \(1\). Minus the square from the two quarter circles and we get \( \pi / 2 - 1\) , same as \( \pi / 4 - 1 / 2\).
      🙂

      Very Interesting

      debbieD amusingmarmosetA 2 Replies Last reply Reply Quote 5
      • debbieD
        debbie ADMIN M0★ M1 M5 @RZ923
        last edited by

        @RZ923 Wow!!!!! That is so cool! I love this solution; thank you for sharing! 🙂 🎉 🎉

        1 Reply Last reply Reply Quote 4
        • debbieD
          debbie ADMIN M0★ M1 M5
          last edited by debbie

          @RZ923 said in Another way to do "Let's practice"?:

          I found another way to do the "Let 's practice" question.
          We can see by symmetry that the almond is a part of the square with side lengths \(1\). It can be made public two overlapping quarter circles with radius \(1\). The overlapping quarter circles each have an area of \( \pi / 4\), making the total \( \pi / 2\). The square, of course, have an area of \(1\). Minus the square from the two quarter circles and we get \( \pi / 2 - 1\) , same as \( \pi / 4 - 1 / 2\).
          🙂

          M2W1D3-ch-part-4-circles-45-degrees-solution2.png

          $$\begin{aligned} \text{ whole almond area } &= 2 \left( \text{ quarter circle areas } \right) - \text{ area of square } \\ &= 2 \left( \frac{1}{4} \pi \right) - 1 \\ &= \frac{1}{2} \pi - 1 \\ \text{ half-almond area } &= \frac{1}{2} \left( \frac{1}{2} \pi - 1 \right) \\ &= \boxed{ \frac{1}{4}\pi - \frac{1}{2} }\\ \end{aligned} $$
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          • amusingmarmosetA
            amusingmarmoset M0★ M1★ M2★ M3★ M4 @RZ923
            last edited by

            @rz923 Cool!

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            • The Blade DancerT
              The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
              last edited by

              OOOOOOOOOOOOOO NOW I KNOW WHAT IT MEANS

              took me four months to get back at module 2 and read this lmao

              The Blade Dancer
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