Step-by-step explanation
We can apply the Cosine Theorem in order to get the value of the Area as shown as follows:

Substituting terms:

Computing the powers:

Computing the argument and adding numbers:

Subtracting numbers:

Applying the square root to both sides:
![c=\sqrt[]{202.295}=14.22](https://img.qammunity.org/2023/formulas/mathematics/college/a7tykikfx3uk6zr3l2xh57cd0365emw1f8.png)
Now, the area of the triangle is given by the Heron's Formula:

![\text{Area of triangle=}\sqrt[]{s(s-a)(s-b)(s-c)}](https://img.qammunity.org/2023/formulas/mathematics/college/mdg2udyx26tompsv0rudgmbowo7h7du7yw.png)
Substituting terms:
![\text{Area of triangle=}\sqrt[]{25.112(25.112-12)(25.112-24)(25.112-14.223)}](https://img.qammunity.org/2023/formulas/mathematics/college/dwuh0qqacx1jhz5sjhezwq2w3cqynzawea.png)
![\text{Area of triangle=}\sqrt[]{25.112(25.112-12)(25.112-24)(25.112-14.223)}](https://img.qammunity.org/2023/formulas/mathematics/college/dwuh0qqacx1jhz5sjhezwq2w3cqynzawea.png)
Multiplying and computing terms:
