# A triangle has sides with lengths: 2, 9, 10. How do you find the area of the triangle using Heron's formula?

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Jim G.
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Jun 27, 2016

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≈ 8.182 square units

#### Explanation:

This is a 2-step process.

Step 1: Calculate half the perimeter (s ) of the triangle.

#color(red)(|bar(ul(color(white)(a/a)color(black)(s=(a+b+c)/2)color(white)(a/a)|)))#

where a , b and c are the 3 sides of the triangle.let a = 2 , b = 9 and c = 10

#rArrs=(2+9+10)/2=21/2=10.5#

Step 2: Calculate the area (A ) using.

#color(red)(|bar(ul(color(white)(a/a)color(black)(A=sqrt(s(s-a)(s-b)(s-c)))color(white)(a/a)|)))#

#A=sqrt(10.5(10.5-2)(10.5-9)(10.5-10))#

#=sqrt(10.5xx8.5xx1.5xx0.5)≈8.182" (3 dec. places) "#

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