Triangle Area Calculation: Given Perimeter 24 and Height 5

To find the area of triangle $\triangle ABC$, follow these steps:

• Step 1: Since the perimeter is 24, and using the side lengths $AB = 8$, $AC = 7$, we calculate the third side $BC$. Using $AB + AC + BC = 24$, we find:
$8 + 7 + BC = 24 \implies BC = 24 - 15 = 9$
• Step 2: Given that the height from point $A$ to base $BC$ is 5, use the triangle area formula:

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

Substituting base $BC = 9$ and height = 5:

$\text{Area} = \frac{1}{2} \times 9 \times 5 = \frac{45}{2} = 22.5$

Therefore, the area of triangle $\triangle ABC$ is $22.5$.