Area of an equilateral triangle?

Question

if the height is 5.382 inches, can someone find the surface area? its been a while since geometry and i dont remember the formulas, thanks!

Answer 1

16.72 inches squared.


Divide an equilateral triangle into two equal right triangles (meaning, draw the height). The right triangles will have angles of 30, 60, 90, right (an equilateral triangle has 3 60 degree angles)?

The ratio of the sides in such a right triangle (the smallest leg being a) is a:a(sq(3)):2a, where 2a is the hypotenuse and a(sq(3)) is the other leg.

The "other leg" in this case is the height. So a, half of the length of the side of the whole equilateral triangle, is 5.382/sq(3).

Multiply this by 2 to get the whole length of the side. We have our base and height.


The area of an equilateral triangle is 1/2bh. b=2(5.382)/sq(3)
h=5.382

Plug those in and you get 16.72.

Answer 2

you can find the area by the half of the (base x height)

if you're working with a equilateral triangle the height will be the same as the height... if it's a 2-D triangle, just do half of the (base x height)

Answer 3

Since the triangle is equilateral, then the ratio of height to the base is sqrt(3):2. So the base of the triangle is 5.382*2/sqrt(3).

Now find the area

A = (1/2)bh
A = (1/2)(5.382*2/sqrt(3))(5.382)
A = 5.382^2/sqrt(3)

A review of 30-60-90 triangles may be helpful.

Answer 4

in an equilateral triangle
h = 1/2 * a * square root of 3 => a = 2h / square root of 3
S = 1/2 h*a = h^2 / square root of 3 = 16.72 squared inch

Answer 5

You need to know the height, then the formula is 1/2xbasexheight.

Answer 6

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Answer 7

http://www.mathwords.com/a/area_equilateral_triangle.htm