Triangle Area Calculation: Finding ADC Area with Given Segments (15cm, 13cm, 5cm)

Using the given data of the triangle's perimeter we will first find the side AD by calculating the sum of all the sides of the triangle:

$AD+9+15=36$

$AD+24=36$

$AD=36-24=12$

Now that we know that AD is equal to 12, we are able to deduce that AD is also the height from BD since it forms a 90-degree angle.

If AD is the height from BD, it is also the height from DC.

Now we can calculate the area of the triangle ADC:

$\frac{AD\times DC}{2}$

$\frac{12\times5}{2}=\frac{60}{2}=30$