# How do you find the exact area of a triangle with a base of square root 30 meters and a height of square root 6 meters?

Jul 6, 2015

You can't find the exact area of this triangle. The approximate area is ${\text{6.71 m}}^{2}$.

#### Explanation:

The formula for the area of a triangle is

$\text{Area" = 1/2 "base"/"height}$ or

$A = \frac{1}{2} b h$

So, for this triangle,

A = 1/2 × sqrt30 "m" × sqrt6 "m"

$= \frac{1}{2} \sqrt{180} {\text{m}}^{2}$

= 1/2 sqrt(36×5) "m"^2

= 1/2 × 6sqrt5 "m"^2

$= 3 \sqrt{5} {\text{m}}^{2}$

This is as close to an exact area as you will get.

The approximate area is

$A = 3 \sqrt{5} {\text{m"^2 = "3 × 2.236 m"^2 = "6.71 m}}^{2}$ (to two decimal places)