Question

Find the area of the triangle ABC. a = 106.6 m b= 75.7 m c= 77.2 m What is the area of the triangle? m2 (Round to the nearest square meter as needed.)

Answer 1

Answer: 2921 square meters

Work Shown

I'll use Heron's Formula.

`s = \text{semi-perimeter}\\\\s = (a+b+c)/(2)\\\\s = (106.6+75.7+77.2)/(2)\\\\s = 129.75\\\\\text{area} = √(s*(s-a)*(s-b)*(s-c))\\\\\text{area} = √(129.75*(129.75-106.6)*(129.75-75.7)*(129.75-77.2))\\\\\text{area} = √(129.75*23.15*54.05*52.55)\\\\\text{area} = √(8531527.21584375)\\\\\text{area} \approx 2920.877816\\\\\text{area} \approx \boldsymbol{2921} \textbf{ square meters}`