• Categories
  • Recent
  • Tags
  • Popular
  • Users
  • Groups
  • Login
Forum — Daily Challenge
  • Categories
  • Recent
  • Tags
  • Popular
  • Users
  • Groups
  • Login

Formula to figure out why the equilateral triangle area formula works

Module 2 Day 1 Challenge Part 1
3
5
71
Loading More Posts
  • Oldest to Newest
  • Newest to Oldest
  • Most Votes
Reply
  • Reply as topic
Log in to reply
This topic has been deleted. Only users with topic management privileges can see it.
  • T
    The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
    last edited by debbie Apr 27, 2020, 12:53 PM Feb 18, 2020, 5:17 PM

    I know Prof. Loh asked for us to figure out why the equilateral triangle area formula works but I can't figure it out. Anyone have any ideas?

    The Blade Dancer
    League of Legends, Valorant: Harlem Charades (#NA1)
    Discord: Change nickname if gay#7585

    M 1 Reply Last reply Feb 19, 2020, 2:34 AM Reply Quote 0
    • T
      The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
      last edited by Feb 18, 2020, 5:24 PM

      Also how does the little question at the end make sense?

      The Blade Dancer
      League of Legends, Valorant: Harlem Charades (#NA1)
      Discord: Change nickname if gay#7585

      M 1 Reply Last reply Feb 19, 2020, 1:48 AM Reply Quote 0
      • D
        debbie ADMIN M0★ M1 M5
        last edited by Feb 19, 2020, 1:15 AM

        This post is deleted!
        1 Reply Last reply Reply Quote 0
        • M
          minji MOD M0 M1 M2 M3 M4 M5 @The Blade Dancer
          last edited by Feb 19, 2020, 1:48 AM

          @TSS-Graviser

          I believe you're talking about the question with similar right triangles! Please correct me if I misunderstood.

          Since it is a bit complicated to calculate the unknown side lengths of the bigger triangle with a hypotenuse of 314, we are using a simple triangle with a hypotenuse of 2. This simple triangle has side lengths of 1, 3 \sqrt{3} 3​ and 2(hypotenuse), as explained by Prof. Loh in the previous example.

          Between two similar triangles (triangles with same angles--in this case, 30°-60°-90°), corresponding sides are proportional to each other. For example, in this problem, the hypotenuse of the bigger triangle is 314 and that of the smaller triangle is 2, which means the sides are scaled up by a factor of 3142=157 \frac{314}{2} = 157 2314​=157. Therefore, for the unknown sides in the bigger triangle, you can multiply the side lengths of the smaller triangle by 157. As I mentioned, the side lengths of the smaller triangle are 1, 3 \sqrt{3} 3​ and 2, so if you multiply each of these numbers by 157, you will get 157, 1573 \sqrt{3} 3​ and 314. This is how Prof. Loh got the side lengths of the bigger triangle for this question.

          Happy Learning!

          The Daily Challenge Team

          1 Reply Last reply Reply Quote 0
          • M
            minji MOD M0 M1 M2 M3 M4 M5 @The Blade Dancer
            last edited by Feb 19, 2020, 2:34 AM

            @TSS-Graviser

            When you calculate the area of an equilateral triangle, you first need to know the height (altitude). In order to do so, you first take half of one side (s2) (\frac{s}{2}) (2s​) and another side (s) (s) (s) and use the pythagorean theorem to solve for the height:

            h=s2−(s2)2 h = \sqrt{s^2-(\frac{s}{2})^2} h=s2−(2s​)2​
            h=s2−s24 h = \sqrt{s^2-\frac{s^2}{4}} h=s2−4s2​​
            h=4s24−s24 h = \sqrt{\frac{4s^2}{4}-\frac{s^2}{4}} h=44s2​−4s2​​
            h=3s24 h = \sqrt{\frac{3s^2}{4}} h=43s2​​
            h=s23 h = \frac{s}{2} \sqrt{3} h=2s​3​

            The original formula for the area of a triangle is A=12(base)×(height) A = \frac{1}{2} (base)\times(height) A=21​(base)×(height). In this case, base=s base = s base=s and height=s23 height = \frac{s}{2} \sqrt{3} height=2s​3​. Now, let's calculate the area!

            A=12(s)⋅(s23) A = \frac{1}{2} (s)\cdot(\frac{s}{2} \sqrt{3}) A=21​(s)⋅(2s​3​)
            A=s24⋅3 A = \frac{s^2}{4} \cdot \sqrt{3} A=4s2​⋅3​
            A=(s2)2⋅3⇒ A = (\frac{s}{2})^2 \cdot \sqrt{3} \Rightarrow A=(2s​)2⋅3​⇒ This is the equilateral triangle area formula!

            Thus, the equilateral triangle area formula comes from the original triangle area formula [A=12(base)×(height)] [A = \frac{1}{2} (base)\times(height)] [A=21​(base)×(height)]. This is why it works!

            Happy Learning,

            The Daily Challenge Team

            1 Reply Last reply Reply Quote 0

            • 1 / 1
            1 / 1
            • First post
              1/5
              Last post
            Daily Challenge | Terms | COPPA