The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.
The sides of the triangle are given as a = 20, b = 15, and c = 25.
We will use Hero's formula to find the area of this triangle.
<h3>What is Heron's formula?</h3>
It is a three-face polygon that consists of three edges and three vertices.
We use Heron's formula to find the area of a triangle with 3 sides:
Herons formula:
Area of a triangle =
Where a, b, and c are sides of a triangle.
And s = semi perimeter of a triangle.
s = ![\frac{a+b+c}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D)
If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.
Let the given sides be:
a = 20, b = 15 and c = 25.
(20 + 15) > 25
(20 + 25) > 15
(15 + 25) > 20 so the given sides are true.
Now,
Semi perimeter of the triangle:
s = (a+b+c) / 2
s = (20+15+25) / 2
s = 60 / 2
s = 30
Putting s = 30 in the area of the triangle.
we get,
Area of the triangle = ![\sqrt{s(s-a)(s-b)(s-c)}\\](https://tex.z-dn.net/?f=%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D%5C%5C)
Area of the triangle = ![\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150](https://tex.z-dn.net/?f=%5Csqrt%7B30%2830-20%29%2830-15%29%2830-25%29%7D%5C%5C%5C%5C%5Csqrt%7B30%5Ctimes10%5Ctimes15%5Ctimes5%7D%5C%5C%5C%5C%5Csqrt%7B22500%7D%5C%5C%5C%5C150)
Thus, the area of a triangle is 150.
Learn more about the Area of triangles here:
brainly.com/question/11952845
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