Respuesta :

CastleRook
To calculate the area of triangle with three sides we use Heron's formula, 
Area=sqrt(s(s-a)(s-b)(s-c))
where:
s=(a+b+c)/2
thus, 
s=(15+10+20)/2
=22.5
hence the area will be:
Area=sqrt(22.5(22.5-15)(22.5-10)(22.5-20)) 
Area=sqrt(22.5*7.5*12.5*2.5)
=sqrt5273.4375
=72.62 mm^2

The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 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 = 15 mm, b = 10 mm, c = 20 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{(15+10+20)}{2} \\s= 22.5[/tex]

Therefore;

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

       = [tex]22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}[/tex]

       =[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]

[tex]= 72.618 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/4125306
  • Heron's Formula:  https://brainly.com/question/10713495

Level: Middle school

Subject; Mathematics  

Topic: Area

Sub-topic: Area of a triangle