Question

find the area and perimeter of 9 cm, 8 cm, and 8cm.

Answer 1

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:** \( \approx 29.8 \, \text{cm}^2 \)