Question

Find the area of a triangle with legs that are: 15mm,10mm,20mm

Answer 1

The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is $72.618 mm^{2}$

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 = $\sqrt{s(s-a)(s-b)(s-c)}$ when given all the sides of the triangle.

            where $s =\frac{(a+b+c)}{2}$

In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm

Therefore, we use the Heron's formula;

Area= $\sqrt{s(s-a)(s-b)(s-c)}$

 $s =\frac{(a+b+c)}{2}$

$s= \frac{(15+10+20)}{2} \\s= 22.5$

Therefore;

Area = $s\sqrt{s(s-a)(s-b)(s-c)}$

       = $22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}$

       =$\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}$

$= 72.618 mm^{2}$

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

Learn more about:

• Perimeter: brainly.com/question/12905000
• Area: brainly.com/question/12905000
• Area of a triangle: brainly.com/question/4125306
• Heron's Formula:  brainly.com/question/10713495

Level: Middle school

Subject; Mathematics  

Topic: Area

Sub-topic: Area of a triangle

Answer 2

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