Geometry note N. Kraj

We want to find the area of an equilateral triangle just knowing a single side we call "a" "a", that means without finding "h" "h" with the Pythagorean theorem.

We know the area of any triangle: - S(delta)="base"×"height"/2 S(delta) = "base" \times "height" / 2

Now, write "h""h" in terms of "a""a" ( for any aa given ):

  • h2+(a/2)2=a2 h^2 + (a/2)^2 = a^2
  • h2+a2/4=a2 h^2 + a^2 /4 = a^2
  • h2×4+a2=a2×4 h^2 \times 4 + a^2 = a^2 \times 4 ( multiply all with 44 )
  • h2=a2×3/4 h^2 = a^2 \times 3 / 4
  • h=a×32 h = \frac{a \times \sqrt{3} }{2}

Now replace hh with the result in the formula:

  • S(delta)=a×(a×3/2)2 S(delta) = \frac{ a \times ( a \times \sqrt{3} /2 ) }{2}

  • S(delta)=a2×34 S(delta) = \frac{ a^2 \times \sqrt{3} }{4}

And you will never need to find "h""h", only to know just "a""a".

#Geometry

Note by Nikolas Кraj
1 year, 12 months ago

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Comments

I found out that this was in brilliant, geometry section, premium version.

I wonder when are they going to make this available only for premium😅.

Nikolas Кraj - 1 year, 11 months ago
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