Question

The sides of an equilateral triangle is 8 cm. Find its area and height.

Answer 1

Given: Side of the equilateral triangle, a = 8 cm

1. Height of an Equilateral Triangle 

Formula for height:

`h = sqrt(3)/2 xx a`

Substitute a = 8:

`h = sqrt(3)/2 xx 8`

`h = 4sqrt(3)`

Now take `sqrt(3) ≈ 1.732`:

h = 4 × 1.732

h = 6.928 cm

Height = 6.928 cm

2. Area of an Equilateral Triangle

Formula:

Area = `sqrt(3)/4 a^2`

Substitute a = 8:

`h = sqrt(3)/4 xx 8^2`

= `sqrt(3)/4 xx 64`

= `16sqrt(3)`

Now substitute `sqrt(3) ≈ 1.732`:

Area = 16 × 1.732

Area = 27.712 cm²