My Math Forum Height and area of a triangle - surd

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 February 27th, 2017, 09:47 AM #1 Newbie   Joined: Feb 2017 From: uk Posts: 6 Thanks: 0 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 07:04 AM.
 February 27th, 2017, 09:59 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,770 Thanks: 1424 $h$ = triangle height $s$ = side length $b$ = base length $h^2 = s^2 - \left(\dfrac{b}{2}\right)^2 \implies h = \sqrt{s^2 - \left(\dfrac{b}{2}\right)^2}$
 February 27th, 2017, 10:06 AM #3 Newbie   Joined: Feb 2017 From: uk Posts: 6 Thanks: 0 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.
 February 27th, 2017, 10:16 AM #4 Math Team   Joined: Jul 2011 From: Texas Posts: 2,770 Thanks: 1424 $h = \sqrt{30^2 - \left(\dfrac{20}{2}\right)^2}$ $h = \sqrt{900 - 100}$ $h = \sqrt{800} = \sqrt{400} \cdot \sqrt{2} = 20\sqrt{2}$
 February 27th, 2017, 10:25 AM #5 Newbie   Joined: Feb 2017 From: uk Posts: 6 Thanks: 0 Thank you! So the area of the triangle will be 282.8? How do I convert that to a surd?
February 27th, 2017, 01:29 PM   #6
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Quote:
 Originally Posted by tenpence 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 ...

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

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

Last edited by skipjack; February 28th, 2017 at 07:06 AM.

February 27th, 2017, 01:33 PM   #7
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Quote:
 Originally Posted by tenpence 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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