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The area can be found using the Heron's formula.


First, divide the sum of the legs by 2.

i.e. s = (6 + 4 + 8)/2 = 18/2 = 9.


The heron's formula is given by


[tex] A=\sqrt{s(s-a)(s-b)(s-c)}\\ \\=\sqrt{9(9-6)(9-4)(9-8)}= \sqrt{9(3)(5)(1)}\\ \\=\sqrt{135}\approx11.6\ square\ units [/tex]

The area of a triangle with legs that are 6 mm, 4 mm, and 8 mm is [tex]11.619 mm^{2}[/tex]

Further Explanation;

Area  

  • Area is a measure of how much space is occupied by a given shape.
  • Area of a substance is determined by the type of shape in question.

For example;

  • Area of a rectangle is given by; Length multiplied by width
  • Area of a circle = πr². where r is the radius of a circle,
  • Area of a square = S², Where s is the side of the square.etc.

Area of a triangle  

  • The area of a triangle is given based on the type of the triangle in question.

Right triangle.

The area of a right triangle is given by;

                    =  1/2 x base x height

Scalene triangle

  • It is a triangle that with sides and angles that are not equal.
  • Area of a scalene triangle depends on the features of the triangle given.

For example;

Sine Formula

  • Area of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between them

Heron's formula

  • Area of a triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle.  

            where [tex]s =\frac{(a+b+c)}{2}[/tex]

In this case we are given, a = 6 mm, b = 4 mm, c = 8 mm

Therefore, we use the Heron's formula;  

Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]  

 [tex]s =\frac{(a+b+c)}{2}[/tex]

[tex]s= \frac{(6+4+8)}{2} \\s= 9[/tex]

Therefore;

Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]  

       = [tex]\sqrt{9(9-6)(9-4)(9-8)}[/tex]  

       =[tex]\sqrt{9(3)(5)(1)} \\\sqrt{135}[/tex]

[tex]= 11.619 mm^{2}[/tex]

Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.

Learn more about:

  • Perimeter: https://brainly.com/question/12905000
  • Area: https://brainly.com/question/12905000
  • Area of a triangle: https://brainly.com/question/4354581
  • Heron's Formula: https://brainly.com/question/4354581
  • Sine Formula: https://brainly.com/question/4354581

Level: Middle school

Subject; Mathematics  

Topic: Area  

Sub-topic: Area of a triangle  

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