Triangle and Area

Question

Triangle ABC is an equilateral triangle with AC =6; find the area of this triangle.

Answer 1

we know the formula of Area of an equilateral triangle is (√3/4)×(side)^2

= (√3/4)× (6)^2

= (√3/4) × 36

= 9√3

Answer 2

Each side = 6

Each angle is 60 degrees. All triangles' angles sum to 180. They all have 3 angles. 180/3 = 60

Put the triangle on one side for its base. Drop a perpendicular vertical line from the top to the base.

That creates 2 right triangles, each with 60-90 and 30 degrees. base of each is 3, hypotenuse = 6

height is 3sqr3 = about 1.732 x 3 = 5.20.

Area is x base(of right triangles) x height = 3 x 5.2 = 15.6

Sin30 = 1/2

Sin60 = sqr3/2

the height of the triangle divided by the hypotenuse = sin60

Let x = the triangle height sin60=x/h = x/6 = sqr3/2

solve for x

cross multiply

2x = 6sqr3

x = 3sqr3

height x base(of the equilateral triangle) = 3sqr3 x 6 =18sqr3 = 31.2

divide by 2 = 15.6