How do you calculate the area of a triangle with sides 5 cm, 7 cm, and 9 cm?

You can calculate the area of a triangle with sides 5 cm, 7 cm, and 9 cm using Heron's formula.

To use Heron's formula, you first need to find the semi-perimeter of the triangle. The semi-perimeter (s) is half the sum of the lengths of the sides. For a triangle with sides a, b, and c, the semi-perimeter is calculated as follows:
\[ s = \frac{a + b + c}{2} \]

For our triangle with sides 5 cm, 7 cm, and 9 cm:
\[ s = \frac{5 + 7 + 9}{2} = \frac{21}{2} = 10.5 \text{ cm} \]

Next, Heron's formula for the area (A) of a triangle is:
\[ A = \sqrt{s(s - a)(s - b)(s - c)} \]

Substitute the values of s, a, b, and c into the formula:
\[ A = \sqrt{10.5 \times (10.5 - 5) \times (10.5 - 7) \times (10.5 - 9)} \]
\[ A = \sqrt{10.5 \times 5.5 \times 3.5 \times 1.5} \]

Now, calculate the product inside the square root:
\[ 10.5 \times 5.5 = 57.75 \]
\[ 57.75 \times 3.5 = 202.125 \]
\[ 202.125 \times 1.5 = 303.1875 \]

Finally, take the square root of 303.1875 to find the area:
\[ A = \sqrt{303.1875} \approx 17.42 \text{ cm}^2 \]

So, the area of the triangle with sides 5 cm, 7 cm, and 9 cm is approximately 17.42 square centimetres.