Question

The side of an equilateral triangle is 6 V3 cm. Find the area of the triangle. [Take V3 = 1.132)​

Answer 1

Answer:

Altitude = Height = 6 cm

Let length of side be 'a'

So , √3/2 a = 6

So a = 12/√3

So a = 4√3 cm

This 'a' is the length of the side

Now, area = (√3/4) × a²

So, Area = (√3/4) × (4√3)²

So, Area = (√3/4) × (16×3)

So, Area = ✓3 × 4 × 3

So, Area = 12√3

So, Area = 12×1.732

Answer 2

Answer:

30.564 cm sq

Step-by-step explanation:

first draw a median from one vertice of the triangle to other side of the triangle

as its an equilateral triangle the median will divid the other side in equal parts and will form a 90° angle with the sides

as it forms 90° we can take the two triangles as right angled triangles

in right angled traingles we can use pythagoras theorem

so acc to it

and let the length of median be x

( 6√3 )² = ( 3√3 )² + x²

108 = 27 + x²

x² = 81

x = 9 cm

we got the height of the triangle as 9 cm

area of triangle = 1/2 * base * height

= 1/2 * 6√3 * 9

= 27√3

= 27 * 1.132

= 30.564 cm²