Question

Find the area of an equilateral triangle whose height is 8 cm.

Answer 1

Given: An equilateral triangle with height h = 8 cm.

Step-wise calculation:

1. For an equilateral triangle, height and side are related by `h = (sqrt(3)/2) xx a`, so `a = (2h)/sqrt(3)`.

2. Using the standard area formula `A = (sqrt3/4) xx a^2`. 

Substitute `a = (2h)/sqrt(3)` to get a height-based formula:

`A = (sqrt(3)/4) xx ((2h)/sqrt3)^2`

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

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

3. Plug h = 8 cm:

`A = (sqrt(3)/3) xx (8^2)`

= `(sqrt(3)/3) xx 64`

= `(64sqrt(3))/3 cm^2`

4. Decimal value (approx.):

`sqrt(3) ≈ 1.732`, so `A ≈ 64 xx 1.732/3 ≈ 36.95  cm^2`.

Area = `(64sqrt(3))/3 cm^2 ≈ 36.95  cm^2`.