tenpence

Hey,

How do I work out the height of an isosceles triangle as a surd? I have the base length and the length of the side.

Then how do I work out the area of a triangle as a surd?

Thanks for any help.

skeeter

$h$ = triangle height

$s$ = side length

$b$ = base length

$h^2 = s^2 - \left(\dfrac{b}{2}\right)^2 \implies h = \sqrt{s^2 - \left(\dfrac{b}{2}\right)^2}$

tenpence

so if my base was 20cm and my side was 30cm.

height (2) = 30(2) - (20/2) (2)

height (2) = 900 - 100

sorry I'm really bad at this.

skeeter

$h = \sqrt{30^2 - \left(\dfrac{20}{2}\right)^2}$

$h = \sqrt{900 - 100}$

$h = \sqrt{800} = \sqrt{400} \cdot \sqrt{2} = 20\sqrt{2}$

tenpence

Thank you!

So the area of the triangle will be 282.8?

How do I convert that to a surd?

skeeter

turn off the calculator and put it away ...

$A = \dfrac{1}{2} \cdot b \cdot h$

$A = \dfrac{1}{2} \cdot 20 \cdot 20\sqrt{2} = 10 \cdot 20\sqrt{2} = 200\sqrt{2} \, \,\text{cm}^2$

aurel5

it's not appropriate to try this (!)