To find the area and the perimeter of a triangle with side lengths of 9 cm, 8 cm, and 8 cm, we can follow these steps:
Step 1: Determine the Perimeter
The perimeter \( P \) of a triangle is the sum of the lengths of its sides.
\[ P = a + b + c \]
where \( a = 9 , \text{cm} \), \( b = 8 , \text{cm} \), and \( c = 8 , \text{cm} \).
\[ P = 9 + 8 + 8 = 25 , \text{cm} \]
Step 2: Determine the Area
To find the area \( A \), we can use Heron's formula. First, we need to calculate the semi-perimeter \( s \):
\[ s = \frac{P}{2} = \frac{25}{2} = 12.5 , \text{cm} \]
Then, we can use Heron's formula:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Now, substitute the values:
\[ A = \sqrt{12.5 \times (12.5 - 9) \times (12.5 - 8) \times (12.5 - 8)} \] \[ = \sqrt{12.5 \times 3.5 \times 4.5 \times 4.5} \] \[ = \sqrt{12.5 \times 3.5 \times 20.25} \] \[ = \sqrt{12.5 \times 70.875} \] \[ = \sqrt{886.09375} \] \[ \approx 29.8 , \text{cm}^2 \]
Summary
- Perimeter: \( 25 , \text{cm} \)
- Area: \( \approx 29.8 , \text{cm}^2 \)