Question

the perimeter of an equilateral triangle 54 cm. find its area.

Answer 1

THe FOrmula to find the perimeter of an equilateral triangle is

3x, where x is the side

3x = 54
x = 54/3

x = 18cm

One side is 18cm

To find the area of an equilateral triangle , we will need to find the height.

If we draw a line from the top vertex to the base line perpendicularly, then, we get the base divided into half, we get the height and yes, we can use pythogoreus theorm.

side - 9
height - x
hypo. - 18

81 + x^2 = 324
x^2 = 243

x = root 243

x = root9 * root27

x = 3 * root9 * root3

x = 3* 3 * root3

x = 9root3

area = 1/2 * base * height

1/2 * 18 *9root3

162root3 /2

$81 \sqrt{3}$
is the area

Hope my answer helps!

Answer 2

let each side of triangle be x
X*X*X=54
3x=54
x=54/3=18

height of equilateral triangle be y


we know,y²+half base square=18²
thus,y²=18²-9²
y²=243
y=9√3


thus,area of triangle=½*18*9√3
=81√3