Find the area of an equilateral triangle with side 12.?

Question

a. 36 /3

b. 72

c. 36

d. 3 /3

Answer 1

a = 12
Area of the equilateral triangle = sqrt 3/4 a^2 sq units
= sqrt 3/4 12^2
= sqrt 3*3*12
= sqrt (3)36....

Answer 2

There are 2 formula that artwork for any triangle, equilateral or no longer. the favored one you're taught is (a million/2)bh. to apply that one, you choose the peak, that's a perpendicular from the right of the triangle to whichever component you have chosen as "base". For an equilateral triangle with component x, that height is h = x * sqrt(3)/2 which you will locate from trigonometry understanding each and all the angles are 60 levels. the backside is likewise x. (Edit: you additionally can use Pythagoras to locate h. it particularly is a suited triangle with hypotenuse x and component x/2, on your case 12 and six) So A = (a million/2)x*x*sqrt(3)/2 = x^2 * sqrt(3)/4 the different formula you ought to use is Heron's formula. it is greater complicated yet has the ease which you do no longer could desire to do any trig. It has 2 factors. - First calculate s = (a + b + c)/2 the place a, b and c are the facets. for this reason a = b = c = x, so s = 3x/2. - Then A = sqrt[s(s - a)(s - b)(s - c)] For the equilateral triangle s - a = s - b = s - c = 3x/2 - x = x/2 So A = sqrt[ (3x/2)(x/2)(x/2)(x/2) ] = sqrt(3x^4/sixteen) = x^2 * sqrt(3)/4 And specific, i've got left it as much as you to plug in the fee of x.

Answer 3

To do this, drop a perpendicular from any point to the opposite side. It will be the height of the triangle, and It will also bisect the base.

Now, that means you will have a right triangle with base of 6 and hypotenuse of 12 (i.e., the side of the orignial triangle). Use the Pythagorean to get the side:

6^2 + h^2 = 12^2
36+h^2= 144
h^2 = 108
h = sqrt(108) = sqrt(36*3) = 6*sqrt(3)

Now, the height of each right triange is: 1/2 * b * h or

1/2*6*6sqrt(3) = 18sqrt(3)

Now, double this to get the whole area, and you get:

36*sqrt(3) which I assume is answer A

Answer 4

It is really easy. There is a formula for finding the area of an equilateral triangle when 1 side is given.

square root of (3) the whole divided by 4 multiplied by the square of the given side.

((root of 3) /4) * 12^2
=36root3 which is option a

Answer 5

12+12=24+12=36
12*3=36
answer*36

Answer 6

All angles are 60°
Area = (1/2) x base x height
Area = (1/2) x 12 x 12.sin 60°
Area = 72.√3/2
Area = 36.√3
Could this be answer a ?

Answer 7

I got "b: 72"

if it's an equalateral triangle then i believe the height should be 12 as well

1/2*b*h - 1/2*12*12

Answer 8

well since each side is 6, the height would be 6^2-3^2=sqrt(27)

so A=1/2(3)(sqrt(27)