How can we find the area of equilateral traingle

Question

How can we find the area of equilateral triangle if we know just the height of equilateral triangle (say 3/2)?

lagomez · Answer

if the height is 3/2 then we can divide the triangle in two 30-60-90 triangles and use the ratio of 1 - sqrt 3 - 2

Bunuel · Answer

Let say the side of an equilateral triangle is b . image017.gif Now, the height of equilateral triangle is also the median, thus it divides the base into half. Half of the base, \frac{b}{2} and height, h , would be the legs of right triangle and the hypotenuse would be the side of this triangle so (\frac{b}{2})^2+h^2=b^2 --> b^2=h^2*\frac{4}{3} --> b=h\frac{2}{\sqrt{3}} --> area=\frac{1}{2}*height* base=\frac{1}{2}*h*h\frac{2}{\sqrt{3}}=\frac{h^2}{\sqrt{3}} Or: as the hight divides the equilateral triangle in two 30-60-90 triangles then the sides of these triangles will be in the ratio 1:\sqrt{3}:2 , so if height (the side opposite 60 degrees) is h then the side of the equilateral triangle (the side opposite 90 degrees) will be h*\frac{2}{\sqrt{3}} and the area=\frac{1}{2}*h*h\frac{2}{\sqrt{3}}=\frac{h^2}{\sqrt{3}} . For more on triangles check Triangles chapter of Math Book. Hope it helps.

How can we find the area of equilateral traingle

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards