Question

Calculate the area and the height of an equilateral triangle whose side is 20 cm

Answer 1

$\mathfrak{AnSwEr}$

Area of an equilateral triangle = $\sf{\frac{\sqrt{3}}{4} a^{2}}$, where a = side of the triangle

By substituting the values, we get the area =》 $\huge{\sf{1000\sqrt{3}\: cm^{2}}}$

We know that :

Area = bh/2

By substituting the values, we get the height =》 $\huge{\sf{100\sqrt{3}\: cm}}$

Answer 2

Solution:-

Given:-

Side of an Equilateral Triangle = 20cm.

To Find :-

Area of an Equilateral Triangle = ?

Height of an Equilateral Triangle = ?

Find :-

We know that,

Area of Equilateral Triangle = ( √3/4)a²

=) Area = [ (√3/4) × 20 × 20 ]

=) Area = [ √3 × 5 × 20 ]

=) Area = 100√3 cm²

Now,

Height of an Equilateral Triangle = [ a√3/2 ]

=) Height = [ 100√3 × √3/2 ]

=) Height = [ 50 × √3 × √3]

=) Height = [ 50 × 3 ]

=) Height = 150 cm.

Identity Used:-

▪ Area of Equilateral Triangle = ( √3/4)a²

▪ Height of an Equilateral Triangle= a√3/2