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Answer :
The area of triangle KLM is approximately 268.77 square units using Heron's formula for triangles with given side lengths.
To find the area of triangle KLM, we can use Heron's formula, which states:
[tex]\[ \text{Area} = \sqrt{s(s - KL)(s - KM)(s - LM)} \][/tex]
where [tex]\( s \)[/tex] is the semi-perimeter of the triangle, calculated as:
[tex]\[ s = \frac{1}{2}(KL + KM + LM) \][/tex]
Given [tex]\( KL = 28 \)[/tex], [tex]\( KM = 28 \)[/tex], and [tex]\( LM = 21 \)[/tex], we can find [tex]\( s \)[/tex] first:
[tex]\[ s = \frac{1}{2}(28 + 28 + 21) = \frac{1}{2}(77) = 38.5 \][/tex]
Now, we can use Heron's formula:
[tex]\[ \text{Area} = \sqrt{38.5(38.5 - 28)(38.5 - 28)(38.5 - 21)} \][/tex]
[tex]\[ = \sqrt{38.5 \times 10.5 \times 10.5 \times 17.5} \][/tex]
[tex]\[ = \sqrt{72277.8125} \][/tex]
[tex]\[ \approx 268.77 \][/tex]
So, the area of triangle KLM is approximately [tex]\( 268.77 \)[/tex] square units.
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