area of triangle is wrong!

[chanansh]

https://cookbook.openai.com/examples/gpt4o/introduction_to_gpt4o
area of triangle in the picture is wrong!

should be

To find the area of a triangle given its three sides, we use **Heron's formula**:

\[
A = \sqrt{s(s-a)(s-b)(s-c)}
\]

where:
- \( a = 5 \), \( b = 6 \), and \( c = 9 \)
- \( s \) is the **semi-perimeter**, calculated as:

\[
s = \frac{a + b + c}{2} = \frac{5 + 6 + 9}{2} = \frac{20}{2} = 10
\]

Now, applying Heron's formula:

\[
A = \sqrt{10(10 - 5)(10 - 6)(10 - 9)}
\]

\[
A = \sqrt{10 \times 5 \times 4 \times 1}
\]

\[
A = \sqrt{200}
\]

\[
A = 10\sqrt{2} \approx 14.14
\]

Thus, the area of the triangle is **\( 10\sqrt{2} \) or approximately 14.14 square units**.

currently:

To find the area of the triangle, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In the triangle you provided:

- The base is \(9\) (the length at the bottom).
- The height is \(5\) (the vertical line from the top vertex to the base).

Now, plug in the values:

\[
\text{Area} = \frac{1}{2} \times 9 \times 5
\]

Calculating this:

\[
\text{Area} = \frac{1}{2} \times 45 = 22.5
\]

Thus, the area of the triangle is **22.5 square units**.