How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #9 #?

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Answer 1 · 2016-02-07T18:11:11

#Area=13.416# square units

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=7, b=4# and #c=9#

#implies s=(7+4+9)/2=20/2=10#

#implies s=10#

#implies s-a=10-7=3, s-b=10-4=6 and s-c=10-9=1#
#implies s-a=3, s-b=6 and s-c=1#

#implies Area=sqrt(10*3*6*1)=sqrt180=13.416# square units

#implies Area=13.416# square units

Answer 2 · 2016-02-23T13:45:35

#13.416. units#

Heron's formula:

#color(blue)(Area=sqrt(s(s-a)(s-b)(s-c))#

Where,

#color(brown)(a-b-c=sides,s=(a+b+c)/2=semiperimeter# #color(brown)(of# #color (brown)(triangle#

So,

#color(red)(a=7#

#color(red)(b=4#

#color(red)(c=9#

#color(red)(s=(7+4+9)/2=20/2=10#

Substitute the values

#rarrArea=sqrt(10(10-7)(10-4)(10-9))#

#rarr=sqrt(10(3)(6)(1))#

#rarr=sqrt(10(18))#

#rarr=sqrt180#

We can further simplify that,

#color(green)(sqrt180=sqrt(36*5)=6sqrt5~~13.416.units#