Question

The height of an equilateral triangle is `3sqrt(3)` cm. Its area is ______.

Options

• `6sqrt(3)` cm²

• 27 cm²

• `9sqrt(3)` cm²

• `27sqrt(3)` cm²

Answer 1

The height of an equilateral triangle is `3sqrt(3)` cm. Its area is `underlinebb(9sqrt(3)  cm^2)`.

Explanation:

`1/2 xx a xx h = sqrt(3)/4 a^2`

⇒ `a = (2h)/sqrt(3)`

= `(2/sqrt(3) xx 3sqrt(3)) cm`

= 6 cm

∴ Area = `(sqrt(3)/4 xx 6 xx 6) cm^2`

= `9sqrt(3)  cm^2`