Question

the height of an equilateral triangle is root 3 a unit.
then its area is equal to

Answer 1

Answer:

let one side of the equilateral triangle be 'x' units

as all the sides in equilateral triangles are equal

area of the triangle = 1/2 × base × height

= 1/2 × (x) × √3

= (x√3)÷2

area of the triangle is = ( x√3)÷2

as the height of an equilateral triangle is also it's median

we can divide the equilateral triangle into two right angled triangles each with height √3 units and

base x/2 and hypotenuse x units

by Pythagoras theorem

( x)^2 =( √3)^2 + (x/2)^2

x^2 = 3 + x^2/4

3= (x^2 /4 ) - x^2

3 = (x^2 -4x^2) ÷ 4

3= -3x^2 ÷ 4

( 3) × (4) = -3x^2

12 = -3x^2

12÷3 = x^2

4 = x^2

x^2 = 4

x = √4

x = 2. ( because length can't be negative)

as previously found

area of the equilateral = x√3 ÷ 2

substitute the value of x= 2

area of the equilateral triangle = 2√3 ÷ 2

= √3 sq units

therefore the area of the equilateral triangle is '√3 sq units'