How do you use Heron's formula to find the area of a triangle with sides of lengths #2 #, #2 #, and #3 #?

Question

2014 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-22T19:40:43

#Area=1.9843# square units

Hero'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=2, b=2# and #c=3#

#implies s=(2+2+3)/2=7/2=3.5#

#implies s=3.5#

#implies s-a=3.5-2=1.5, s-b=3.5-2=1.5 and s-c=3.5-3=0.5#
#implies s-a=1.5, s-b=1.5 and s-c=0.5#

#implies Area=sqrt(3.5*1.5*1.5*0.5)=sqrt3.9375=1.9843# square units

#implies Area=1.9843# square units

Answer 2 · 2016-01-22T19:40:53

Area = 1.98 square units

enter image source here

First we would find S which is the sum of the 3 sides divided by 2.

#S = (2 + 2 + 3)/2 # = #7/2# = 3.5

Then use Heron's Equation to calculate the area.

#Area = sqrt(S(S-A)(S-B)(S-C)) #

#Area = sqrt(3.5(3.5-2)(3.5-2)(3.5-3)) #

#Area = sqrt(3.5(1.5)(1.5)(0.5)) #

#Area = sqrt(3.9375) #

#Area = 1.98 units^2 #