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# https://vle.mathswatch.co.uk/images/questions/question809.png

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https://vle.mathswatch.co.uk/images/questions/question809.png

jakeharris02  Nov 4, 2017
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Because it is an iscocoles triangle, we know two sides are 13 and one side is 10.

Using heron's fomula: http://www.mathwarehouse.com/geometry/triangles/area/herons-formula-triangle-area.php

supermanaccz  Nov 4, 2017
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Thanks, sm!!!!.... we could use Heron's here, but here's a slightly easier approach...IMHO...!!!

Draw an altitude of the triangle......and the altitude of an isosceles triangle will divide the base in half

So....we will have two right triangles

Looking at either of these.....they will have a hypotenuse of 13cm and one leg = 1/2 of the base   = 5cm

And the other leg will  be   sqrt (13^2 - 5^2)  = sqrt (144)  = 12cm  = the height (altitude) of the triangle

So....the area  is

1 / 2  base  * height  =

5 cm  *  12 cm  =

60 cm^2

CPhill  Nov 4, 2017
edited by CPhill  Nov 4, 2017

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