If the value of a side of a equilateral triangle is 10 then what will be the area of the triangle

Question

I want to know the answer.

So please answer it.

Answer 1

base = 10

height = 5*root(3)

Area= 1/2 * base * height= 25*root(3)

Answer 2

here are two approaches...

draw a diagram with the altitude drawn

the altitude divides the triangle into two congruent 30-60-90 right triangles

in this 30-60-90 right triangle the hypotenuse is 10, the shorter leg is 5 because the altitude bisects the side it is drawn to (also it is opposite the 30º angle so it is half of the hypotenuse), and the longer leg is always the length of the shorter side times √3, so the longer side, which is the altitude, is 5√3

A=(1/2)(b)(h)

A=(1/2)(10)(5√3)

A=(5)(5√3)

A=25√3

A=25*1.732

A=43.3 units squared

 

another approach is to use the formula A=absinC/2 where a and b are both 10 and angle C=60º

A=(10)(10)(sin60º)/2

A=(10)(10)( 0.866)/2

A=(100)(0.866)/2

A=86.6/2

A=43.3 units squared

if you want more accuracy use, use more digits in sin60º