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?

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Answer 1 · 2015-07-06T22:20:22

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

The formula for the area of a triangle is

$"Area" = 1/2 "base"/"height"$ or

$A = 1/2 bh$

So, for this triangle,

$A = 1/2 × sqrt30 "m" × sqrt6 "m"$

$= 1/2sqrt180 "m"^2$

$= 1/2 sqrt(36×5) "m"^2$

$= 1/2 × 6sqrt5 "m"^2$

$= 3sqrt5 "m"^2$

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

The approximate area is

$A = 3sqrt5 "m"^2 = "3 × 2.236 m"^2 = "6.71 m"^2$ (to two decimal places)