## How to Find the Area of a triangle having three side

A triangle is a basic and well-known polygon diagram in geometry that has three sides ( a, b and c ) and 3 vertices ( A, B, and C ).

## What is the area of a triangle?

The total region surrounded by the three sides of any specific triangle is known as the area of a triangle.

There are different formulas to find the triangle area, used according to the known and unknown sides.

When base and height are known: Area of triangle = ½ × b × h

**(SSS)**: Area = 0.25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c))

**SAS:** Area = 0.5 × a × b × sin (γ)

**ASA**: Area = a² × sin (β) × sin (γ) / (2 × sin (β + γ))

We’re going to discuss the example to understand how to find the area of a triangle.

**Example :**

Calculate the area of a triangle having three sides of 7 cm, 5 cm, and 11 cm respectively.

**Solution:**

Because we have all three sides of a triangle, we will use the SSS formula (Heron’s formula) given above.

**Step 1**: Identify and write down the given values.

a = 7 cm, b = 5 cm, c = 11 cm

**Step 2**: Write down the triangle area heron’s formula.

Area = 0.25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c))

**Step 3**: Substitute the given values and calculate the area.

Area = 0.25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c))

Area = 0.25 × √ ((7 + 5 + 11) × (-7 + 5 + 11) × (7 - 5 + 11) × (7 + 5 - 11))

Area = 0.25 × √ ((23) × (9) × (13) × (1))

Area = 0.25 × √ (2691)

Area = 12.97 cm2

So, the area of a triangle with three sides of 7 cm, 5 cm, and 11 cm is 12.97 cm2.