One side of an equilateral triangle is 6in. Find the area of the trianlge.?

Using 30-60-90 degree special triangle properties,

height = 3sqrt(3)

area = (1/2)(6)[3sqrt(3)] = 9sqrt(3) units^2

Divide the triangle into two 30-60-90 triangles. The sides of a 30-60-90 triangle have the proportions 1:2:√3, so these triangles have sides 3, 6, and 3√3.

Area of both triangles is base times the height, or

9√3 in²

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An equilateral triangle is divided into two equal right triangles by dropping an altitude from any vertex to the opposite side. The hypotenuse of each right triangle is a side of the equilateral triangle, and one leg will be half of a side, so the altitude can be expressed as:

h = sqrt(s^2 - (s/2)^2) = sqrt(3s^2/4) = s*sqrt(3)/2 using the formula for the area of a triangle A = bh/2 and substituting we have:

A = s * s * sqrt(3)/4 = 6 * 6 sqrt(3)/4 = 9sqrt(3) = 15.59 sq. inches.

Since its an equilateral triangle all sides are 6in and all angles 60

height^2=6^2-3^2=36-9=27=9*3

height=3sqr3

Area=6*3*sqr3*1/2=9sqr3=15.6

The area is 15.6 square inches

Area = 0.5absinC

That is the sin of one of the angles times by the remaining sides i.e the sides that are not opposite the angle 'C' hence the reason for know 'c'.

Dont really have to worry about this for equalateral triangle for obvious reasons

So it would be

Area = 0.5 x 6 x 6 x sin60

= 15.588 In (3dp)

since the triangle is equilateral all angles are 60 degrees

area= 1/2 x 6 x 6x sin60deg =15.6 in^2

You need to use trig to find the height of the triangle, which is 6*sin(60) because the adjacent side is length 60 and the angle is 60.

6*sin(60)=6*sqrt(3)/2=3*sqrt(3)

Now, use A=1/2b*h = (1/2)*(6)*(3sqrt(3)) = 9 sqrt(3) square inches.

area of equilateral triangle = (square root of 3)/4 x (a)square

where a=6in

if one side is 6in then all sides are 6in

Herons Formula is a formula for working the area of a triangle where all 3 sides are known

it is :

A=sqrt(s(s-a)(s-b)(s-c))

for all triangles abc

where s=(a+b+c)/2

so in this case the answer is:

s=(6+6+6)/2=9

A=sqrt(9(9-6)(9-6)(9-6))

=sqrt(9(3)(3)(3))

=sqrt(243)

=9root3 in^2

the area of an equalaterla triangle is the square root of 3 multiplied by the side squared, then that answer divided by 4