Question

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

Answer 1

Answer:

Area = $\frac{75}{4} \sqrt{15} sq mm$

Step-by-step explanation:

Here we are given with all the sides of the triangle , and we are asked to find the area of it. we will use Heron's Formula to find the area. The formula is as under

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

Where $s= \frac{a+b+c}{2}$

Where a , b and c are the three sides of the triangle

a=15 , b=10 and c=20

Substituting those values in the two formula one by one we get

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

$s=\frac{45}{2}$

now putting this value of s in main formula we get

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

Area = $\sqrt{\frac{45}{2} \times (\frac{45}{2}-15) \times (\frac{45}{2}-10) \times (\frac{45}{2}-20)}$

Area = $\sqrt{\frac{45}{2} \times (\frac{45-30}{2}) \times (\frac{45-20}{2}-) \times (\frac{45-40}{2})}$

Area = $\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{25}{2}) \times (\frac{5}{2})}$

Area = $\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{20}{2}-) \times (\frac{5}{2})}$

Area = $\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}$

Area = $\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}$

Area = $\frac{1}{4} \sqrt{9 \times 5 \times 5 \times 3 \times 25 \times 5}$

Area = $\frac{3\times 5 \times 5}{4} \sqrt{3 \times5}$

Area = $\frac{75}{4} \sqrt{15}$

Answer 2

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

 $s =\frac{(a+b+c)}{2}$

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

Therefore;

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

       = $22.5\sqrt{12.5(12.5-15)(22.5-10)(22.5-20)}$

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

$= 72.618 mm^{2}$

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

Learn more about:

• Perimeter: 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

• Example of a question using Heron's Formula:  https://brainly.com/question/10713495

Level: Middle school

Subject; Mathematics  

Topic: Area

Sub-topic: Area of a triangle