Answer:
To find the area of a triangle given the lengths of its sides, you can use Heron's formula.
First, calculate the semi-perimeter of the triangle (\( s \)):
\[ s = \frac{KL + LM + KM}{2} \]
In this case, \( KL = LM = 13 \) inches and \( KM = 10 \) inches:
\[ s = \frac{13 + 13 + 10}{2} = 18 \text{ inches} \]
Now, use Heron's formula to find the area (\( A \)) of the triangle:
\[ A = \sqrt{s \cdot (s - KL) \cdot (s - LM) \cdot (s - KM)} \]
Substitute the values:
\[ A = \sqrt{18 \cdot (18 - 13) \cdot (18 - 13) \cdot (18 - 10)} \]
\[ A = \sqrt{18 \cdot 5 \cdot 5 \cdot 8} \]
\[ A = \sqrt{3600} = 60 \text{ square inches} \]
Therefore, the area of △KLM is 60 square inches.
