How do you use Heron's formula to determine the area of a triangle with sides of that are 8, 3, and 10 units in length?

Question

1140 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-10T15:14:43

Area of triangle is #9.922#

According to Heron's formula, if the sides of a triangle are #a#, #b# and #c#, then the area of the triangle #Delta# is given by the formula

#Delta=sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)#

Here we have three sides of a triangle as #8#, #3# and #10#.

Hence #s=1/2(8+3+10)=1/2xx21=21/2#

and #Delta=sqrt(21/2(21/2-8)(21/2-3)(21/2-10))#

= #sqrt(21/2xx5/2xx15/2xx1/2)#

= #1/4sqrt(3xx7xx5xx3xx5)#

= #15/4xxsqrt7#

= #15/4xx2.6458#

= #9.922#