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2 years ago

Find the area a of the triangle whose sides have the given lengths. a = 20, b = 15, c = 25 a =?

Mathematics

1 answer:

PIT_PIT [208]2 years ago

3 0

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

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

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

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

Area of the triangle = $\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150$

Thus, the area of a triangle is 150.

Learn more about the Area of triangles here:

brainly.com/question/11952845

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