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February 27th, 2017, 10:47 AM   #1
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Height and area of a triangle - surd

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.

Last edited by skipjack; February 28th, 2017 at 08:04 AM.
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February 27th, 2017, 10:59 AM   #2
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$h$ = triangle height

$s$ = side length

$b$ = base length

$h^2 = s^2 - \left(\dfrac{b}{2}\right)^2 \implies h = \sqrt{s^2 - \left(\dfrac{b}{2}\right)^2}$
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February 27th, 2017, 11:06 AM   #3
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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.
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February 27th, 2017, 11:16 AM   #4
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$h = \sqrt{30^2 - \left(\dfrac{20}{2}\right)^2}$

$h = \sqrt{900 - 100}$

$h = \sqrt{800} = \sqrt{400} \cdot \sqrt{2} = 20\sqrt{2}$
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February 27th, 2017, 11:25 AM   #5
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Thank you!

So the area of the triangle will be 282.8?

How do I convert that to a surd?
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February 27th, 2017, 02:29 PM   #6
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Quote:
Originally Posted by tenpence View Post
Thank you!

So the area of the triangle will be 282.8?

How do I convert that to a surd?
turn off the calculator and put it away ...

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

$A = \dfrac{1}{2} \cdot 20 \cdot 20\sqrt{2} = 10 \cdot 20\sqrt{2} = 200\sqrt{2} \, \,\text{cm}^2$
Thanks from greg1313, topsquark and aurel5

Last edited by skipjack; February 28th, 2017 at 08:06 AM.
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February 27th, 2017, 02:33 PM   #7
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Quote:
Originally Posted by tenpence View Post

So the area of the triangle will be 282.8?

How do I convert that to a surd?

it's not appropriate to try this (!)
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