How do you use Heron's formula to find the area of a triangle with sides of lengths #1 #, #2 #, and #2 #?

Question

3101 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-29T15:19:23

#Area=0.9682458366# square units

enter image source here
Heron's formula for finding area of the triangle is given by
#Area=sqrt(s(s-a)(s-b)(s-c))#

Where #s# is the semi perimeter and is defined as
#s=(a+b+c)/2#

and #a, b, c# are the lengths of the three sides of the triangle.

Here let #a=1, b=2# and #c=2#

#implies s=(1+2+2)/2=5/2=2.5#

#implies s=2.5#

#implies s-a=2.5-1=1.5, s-b=2.5-2=0.5 and s-c=2.5-2=0.5#
#implies s-a=1.5, s-b=0.5 and s-c=0.5#

#implies Area=sqrt(2.5*1.5*0.5*0.5)=sqrt0.9375=0.9682458366# square units

#implies Area=0.9682458366# square units