Respuesta :
Answer:
Area of the triangle is 4.8 square meters using heron's formula to find area of triangle.
Step-by-step explanation:
Formula to find area of triangle when three sides were given is
Semi perimeter s =[tex]\frac{a+b+c}{2}[/tex]
Where 'a' , 'b' and 'c' are side lengths of the triangle.
Area =[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Here, let a=2, b=4.8 and c=5.2
So, semi perimeter s=[tex]\frac{2+4.8+5.2}{2}[/tex]
Simplify it
s=6
Now use area formula to find area of the triangle.
A=[tex]\sqrt{6(6-2)(6-4.8)(6-5.2)}[/tex]
Simplify it
A=[tex]\sqrt{6(4)(1.2)(0.8)}[/tex]
A=[tex]\sqrt{23.04}[/tex]
A=4.8 square meters.
To find the area of a triangle with the given sides a, b and c we use an expression,
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where, [tex]s=\frac{a+b+c}{2}[/tex]
By applying this formula area of the given triangle is 4.8 m².
Side lengths of the triangle are 2m, 4.8m and 5.2m
Therefore, [tex]s=\frac{2+4.8+5.2}{2}[/tex]
[tex]s=6[/tex]
Now substitute these values in the formula,
Area = [tex]\sqrt{6(6-2)(6-4.8)(6-5.2)}[/tex]
= [tex]\sqrt{6(4)(1.2)(0.8)}[/tex]
= 4.8 m²
Therefore, area of the triangle with the given sides is 4.8 m².
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