To find the area of a triangle when given the lengths of its sides, we can use Heron's formula, since you provided three sides (6 cm, 5 cm, and 8 cm).
-
First, calculate the semi-perimeter (s) of the triangle: \[ s = \frac{a + b + c}{2} = \frac{6 + 5 + 8}{2} = \frac{19}{2} = 9.5 , \text{cm} \]
-
Next, apply Heron's formula to find the area (A): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] where \(a = 6\) cm, \(b = 5\) cm, and \(c = 8\) cm.
-
Calculate each term:
- \(s - a = 9.5 - 6 = 3.5\)
- \(s - b = 9.5 - 5 = 4.5\)
- \(s - c = 9.5 - 8 = 1.5\)
-
Substitute these values into the formula: \[ A = \sqrt{9.5 \times 3.5 \times 4.5 \times 1.5} \]
-
Now calculate the product: \[ 9.5 \times 3.5 = 33.25 \] \[ 33.25 \times 4.5 = 149.625 \] \[ 149.625 \times 1.5 = 224.4375 \]
-
Finally, take the square root: \[ A \approx \sqrt{224.4375} \approx 15 , \text{cm}^2 \]
Therefore, the area of the triangle is approximately: \[ A \approx 15 , \text{cm}^2 \]